Positive Solutions for a Class of Fractional p-Laplacian Equation with Critical Sobolev Exponent and Decaying Potentials
In this paper, we study the existence of positive solution for the p -Laplacian equations with fractional critical nonlinearity { ( − Δ ) p s u + V ( x ) | u | p − 2 u = K ( x ) f ( u ) + P ( x ) | u | p s ∗ − 2 u , x ∈ ℝ N , u ∈ D s , p ( ℝ N ) , where s ∈ ( 0 , 1 ) , p s ∗ = N p N − s p , N > s...
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| Published in | Acta Mathematicae Applicatae Sinica Vol. 38; no. 2; pp. 463 - 483 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2022
Springer Nature B.V |
| Edition | English series |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper, we study the existence of positive solution for the
p
-Laplacian equations with fractional critical nonlinearity
{
(
−
Δ
)
p
s
u
+
V
(
x
)
|
u
|
p
−
2
u
=
K
(
x
)
f
(
u
)
+
P
(
x
)
|
u
|
p
s
∗
−
2
u
,
x
∈
ℝ
N
,
u
∈
D
s
,
p
(
ℝ
N
)
,
where
s
∈
(
0
,
1
)
,
p
s
∗
=
N
p
N
−
s
p
,
N
>
s
p
,
p
>
1
and
V
(
x
),
K
(
x
) are positive continuous functions which vanish at infinity,
f
is a function with a subcritical growth, and
P
(
x
) is bounded, nonnegative continuous function. By using variational method in the weighted spaces, we prove the above problem has at least one positive solution. |
|---|---|
| AbstractList | In this paper, we study the existence of positive solution for the
p
-Laplacian equations with fractional critical nonlinearity
{
(
−
Δ
)
p
s
u
+
V
(
x
)
|
u
|
p
−
2
u
=
K
(
x
)
f
(
u
)
+
P
(
x
)
|
u
|
p
s
∗
−
2
u
,
x
∈
ℝ
N
,
u
∈
D
s
,
p
(
ℝ
N
)
,
where
s
∈
(
0
,
1
)
,
p
s
∗
=
N
p
N
−
s
p
,
N
>
s
p
,
p
>
1
and
V
(
x
),
K
(
x
) are positive continuous functions which vanish at infinity,
f
is a function with a subcritical growth, and
P
(
x
) is bounded, nonnegative continuous function. By using variational method in the weighted spaces, we prove the above problem has at least one positive solution. In this paper, we study the existence of positive solution for the p-Laplacian equations with fractional critical nonlinearity {(−Δ)psu+V(x)|u|p−2u=K(x)f(u)+P(x)|u|ps∗−2u,x∈ℝN,u∈Ds,p(ℝN), where s∈(0,1),ps∗=NpN−sp,N>sp,p>1 and V(x), K(x) are positive continuous functions which vanish at infinity, f is a function with a subcritical growth, and P(x) is bounded, nonnegative continuous function. By using variational method in the weighted spaces, we prove the above problem has at least one positive solution. |
| Author | He, Xiao-ming Li, Na |
| Author_xml | – sequence: 1 givenname: Na surname: Li fullname: Li, Na organization: College of Science, Minzu University of China – sequence: 2 givenname: Xiao-ming surname: He fullname: He, Xiao-ming email: xmhe923@126.com organization: College of Science, Minzu University of China |
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| Keywords | 35J62 Variational methods 35J50 Mountain Pass Theorem 35B65 Fractional Critical growth Vanishing potential Laplacian |
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| References | Lindgren, Lindqvist (CR31) 2014; 49 Felmer, Quaas, Tan (CR23) 2012; 142 Alves, Souto (CR1) 2013; 254 Brasco, Parini, Squassina (CR9) 2016; 36 (CR30) 2016; 23 (CR36) 2016; 55 Bonheure, Schaftingen (CR8) 2010; 189 Brasco, Mosconi, Squassina (CR10) 2016; 55 Li, Li, Teng, Wu (CR29) 2017; 14 Ambrosio, Isernia (CR7) 2018; 38 Iannizzotto, Squassina (CR27) 2014; 88 Nezza, Palatucci, Valdinoci (CR20) 2012; 136 Brasco, Parini (CR11) 2016; 9 Brezis, Nirenberg (CR13) 1983; 36 Di Castro, Kuusi, Palatucci (CR16) 2014; 267 Iannizzotto, Mosconi, Squassina (CR25) 2016; 32 Ambrosio, Figueiredo, Isernia (CR6) 2020; 199 Rabinowitz (CR39) 1992; 43 Opic, Kufner (CR37) 1990 Caffarelli, Silvestre (CR14) 2007; 32 Mercuri, Willem (CR34) 2010; 28 Ambrosetti, Wang (CR4) 2005; 18 Torres (CR38) 2017; 16 CR5 Deng, Guo, Wang (CR18) 2003; 54 Molica Bisci, Rǎdulescu, Servadei (CR35) 2016 Mawhin, Bisci (CR33) 2017; 95 Dipierro, Medina, Peral, Valdinoci (CR21) 2017; 153 Ambrosetti, Rabinowitz (CR3) 1973; 14 Ambrosetti, Felli, Malchiodi (CR2) 2005; 7 Castro, Kuusi, Palatucci (CR15) 2016; 33 Iannizzotto, Liu, Perera, Squassina (CR26) 2014; 9 do Ó, Miyagaki, Squassina (CR22) 2016; 18 Del Pezzo, Quaas (CR19) 2017; 263 Franzina, Palatucci (CR24) 2014; 5 CR40 Zhu (CR41) 1990; 31 Brezis, Lieb (CR12) 1983; 88 Deng, Li, Shuai (CR17) 2016; 36 Luo, Tang, Li (CR32) 2017; 21 Li (CR28) 1994; 14 A Iannizzotto (1090_CR25) 2016; 32 V Ambrosio (1090_CR6) 2020; 199 A Di Castro (1090_CR16) 2014; 267 L M Del Pezzo (1090_CR19) 2017; 263 1090_CR40 1090_CR5 P Rabinowitz (1090_CR39) 1992; 43 Y Deng (1090_CR17) 2016; 36 (1090_CR30) 2016; 23 A Ambrosetti (1090_CR4) 2005; 18 G Li (1090_CR28) 1994; 14 A Iannizzotto (1090_CR27) 2014; 88 A Ambrosetti (1090_CR2) 2005; 7 P Felmer (1090_CR23) 2012; 142 L Caffarelli (1090_CR14) 2007; 32 E Lindgren (1090_CR31) 2014; 49 G Molica Bisci (1090_CR35) 2016 (1090_CR36) 2016; 55 CE Torres (1090_CR38) 2017; 16 L Brasco (1090_CR9) 2016; 36 L Brasco (1090_CR10) 2016; 55 X Zhu (1090_CR41) 1990; 31 S Dipierro (1090_CR21) 2017; 153 C Mercuri (1090_CR34) 2010; 28 A Ambrosetti (1090_CR3) 1973; 14 H Brezis (1090_CR12) 1983; 88 Y Deng (1090_CR18) 2003; 54 E Nezza (1090_CR20) 2012; 136 H Luo (1090_CR32) 2017; 21 JM do Ó (1090_CR22) 2016; 18 D Bonheure (1090_CR8) 2010; 189 G Franzina (1090_CR24) 2014; 5 A Iannizzotto (1090_CR26) 2014; 9 A D Castro (1090_CR15) 2016; 33 L Brasco (1090_CR11) 2016; 9 J Mawhin (1090_CR33) 2017; 95 C Alves (1090_CR1) 2013; 254 V Ambrosio (1090_CR7) 2018; 38 Q Li (1090_CR29) 2017; 14 B Opic (1090_CR37) 1990 H Brezis (1090_CR13) 1983; 36 |
| References_xml | – volume: 14 start-page: 64 year: 1994 end-page: 74 ident: CR28 article-title: The existence of a weak solution of quasilinear elliptic equation with critical Sobolev exponent on unbounded domain publication-title: Acta Math. Sci. doi: 10.1016/S0252-9602(18)30091-2 contributor: fullname: Li – volume: 55 issue: 4 year: 2016 ident: CR36 publication-title: Calc. Var. Partial Differential Equations – volume: 32 start-page: 1353 year: 2016 end-page: 1392 ident: CR25 article-title: Global Hölder regularity for the fractional -Laplacian publication-title: Rev. Mat. Iberoam. doi: 10.4171/RMI/921 contributor: fullname: Squassina – volume: 36 start-page: 1813 year: 2016 end-page: 1845 ident: CR9 article-title: Stability of variational eigenvalues for the fractional -Laplacian publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2016.36.1813 contributor: fullname: Squassina – volume: 54 start-page: 1121 year: 2003 end-page: 1151 ident: CR18 article-title: Nodal solutions for -Laplace equations with critical growth publication-title: Nonlin. Analysis, TMA. doi: 10.1016/S0362-546X(03)00129-9 contributor: fullname: Wang – start-page: 162 year: 2016 ident: CR35 publication-title: Variational Methods for Nonlocal Fractional Problems doi: 10.1017/CBO9781316282397 contributor: fullname: Servadei – volume: 189 start-page: 273 year: 2010 end-page: 301 ident: CR8 article-title: Van. Ground states for the nonlinear Schrödinger equation with potentials vanishing at infinitly publication-title: Annali Mat. Pura Appl. doi: 10.1007/s10231-009-0109-6 contributor: fullname: Schaftingen – volume: 38 start-page: 5835 year: 2018 end-page: 5881 ident: CR7 article-title: Multiplicity results for nonlinear Schrödinger Equations with the fractional -Laplacian publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2018254 contributor: fullname: Isernia – volume: 43 start-page: 270 year: 1992 end-page: 291 ident: CR39 article-title: On a class of nonlinear Schrödinger equations publication-title: Z. Angew. Math. Phys. doi: 10.1007/BF00946631 contributor: fullname: Rabinowitz – volume: 14 start-page: 349 year: 1973 end-page: 381 ident: CR3 article-title: Dual varitional methods in critical point theory and applications publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(73)90051-7 contributor: fullname: Rabinowitz – volume: 9 start-page: 323 year: 2016 end-page: 355 ident: CR11 article-title: The second eigenvalue of the fractional -Laplacian publication-title: Adv. Calc. Var. doi: 10.1515/acv-2015-0007 contributor: fullname: Parini – volume: 136 start-page: 521 year: 2012 end-page: 573 ident: CR20 article-title: Hitchhiker’s guide to the fractional Sobolev spaces publication-title: Bull. Sci. Math. doi: 10.1016/j.bulsci.2011.12.004 contributor: fullname: Valdinoci – volume: 88 start-page: 233 year: 2014 end-page: 245 ident: CR27 article-title: Weyl-type laws for fractional -eigenvalue problems publication-title: Asymptot. Anal. TMA contributor: fullname: Squassina – volume: 49 start-page: 795 year: 2014 end-page: 826 ident: CR31 article-title: Fractional eigenvalues publication-title: Calc. Var. Partial Differential Equations doi: 10.1007/s00526-013-0600-1 contributor: fullname: Lindqvist – volume: 32 start-page: 1245 year: 2007 end-page: 1260 ident: CR14 article-title: An extension problem related to the fractional Laplacian publication-title: Comm. Partial Differential Equations doi: 10.1080/03605300600987306 contributor: fullname: Silvestre – volume: 18 start-page: 1550063 issue: 06 year: 2016 ident: CR22 article-title: Critical and subcritical fractional problems with vanishing potentials publication-title: Commun. Contemp. Math. doi: 10.1142/S0219199715500637 contributor: fullname: Squassina – volume: 142 start-page: 1237 year: 2012 end-page: 1262 ident: CR23 article-title: Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian publication-title: Proc. Roy. Soc. Edinburgh Sect. A doi: 10.1017/S0308210511000746 contributor: fullname: Tan – volume: 33 start-page: 1279 year: 2016 end-page: 1299 ident: CR15 article-title: Local behavior of fractional -minimizers publication-title: Ann. Inst. H. Poincaré Anal. Non Linéaire doi: 10.1016/j.anihpc.2015.04.003 contributor: fullname: Palatucci – volume: 153 start-page: 183 year: 2017 end-page: 230 ident: CR21 article-title: Bifurcation results for a fractional elliptic equation with critical exponent in ℝ publication-title: Manuscripta Math. doi: 10.1007/s00229-016-0878-3 contributor: fullname: Valdinoci – volume: 18 start-page: 1321 year: 2005 end-page: 1332 ident: CR4 article-title: Nonlinear Schrödinger equations with vanishing and decaying potential publication-title: Diff. Integ. Eqns. contributor: fullname: Wang – ident: CR40 – volume: 7 start-page: 117 year: 2005 end-page: 144 ident: CR2 article-title: Ground states of nonlinear Schrödinger equations with potentials vanishing at infinitly publication-title: J. Eur. Math. Soc. doi: 10.4171/JEMS/24 contributor: fullname: Malchiodi – volume: 254 start-page: 1977 year: 2013 end-page: 1991 ident: CR1 article-title: Existence of solutions for a class of nonlinear Schrödinger equations with potentials vanishing at infinitly publication-title: J. Differential Equations doi: 10.1016/j.jde.2012.11.013 contributor: fullname: Souto – volume: 88 start-page: 486 year: 1983 end-page: 490 ident: CR12 article-title: A relation between pointwise convergence of functions and convergence of functionals publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1983-0699419-3 contributor: fullname: Lieb – volume: 31 start-page: 1161 year: 1990 end-page: 1181 ident: CR41 article-title: Nontrivial solution of quasilinear elliptic equation involving critical Sobolev exponent publication-title: Sci. Sinica. contributor: fullname: Zhu – volume: 36 start-page: 437 year: 1983 end-page: 477 ident: CR13 article-title: Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents publication-title: Commun. Pure. Appl. Math. doi: 10.1002/cpa.3160360405 contributor: fullname: Nirenberg – volume: 263 start-page: 765 year: 2017 end-page: 778 ident: CR19 article-title: A Hopf’s lemma and a strong minimum principle for the fractional -Laplacian publication-title: J. Differential Equations doi: 10.1016/j.jde.2017.02.051 contributor: fullname: Quaas – volume: 28 start-page: 469 year: 2010 end-page: 493 ident: CR34 article-title: A global compactness result for the -Laplacian involving critical nonlinearities publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2010.28.469 contributor: fullname: Willem – volume: 95 start-page: 73 year: 2017 end-page: 93 ident: CR33 article-title: A Brezis-Nirenberg type result for a nonlocal fractional operator publication-title: J. London Math. Soc. (2) doi: 10.1112/jlms.12009 contributor: fullname: Bisci – volume: 199 start-page: 317 year: 2020 end-page: 344 ident: CR6 article-title: Existence and concentration of positive solutions for -fractional Schrödinger equations publication-title: Ann. Mat. Pura Appl. doi: 10.1007/s10231-019-00880-7 contributor: fullname: Isernia – volume: 21 start-page: 1017 year: 2017 end-page: 1035 ident: CR32 article-title: Multiple Solutions of Nonlinear Schrödinger Equation with the Fractional -Laplacian publication-title: Taiwan. J. Math. doi: 10.11650/tjm/7947 contributor: fullname: Li – volume: 9 start-page: 101 year: 2014 end-page: 125 ident: CR26 article-title: Existence results for fractional -Laplacian problems via Morse theory publication-title: Adv. Calc. Var. contributor: fullname: Squassina – volume: 16 start-page: 99 year: 2017 end-page: 113 ident: CR38 article-title: Existence and symmetry result for fractional -Laplacian in publication-title: Commun. Pure Appl. Anal. doi: 10.3934/cpaa.2017004 contributor: fullname: Torres – volume: 267 start-page: 1807 year: 2014 end-page: 1836 ident: CR16 article-title: Nonlocal Harnack inequalities publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2014.05.023 contributor: fullname: Palatucci – volume: 23 issue: 5 year: 2016 ident: CR30 publication-title: Nonlinear Diff. Equat. Appl. – ident: CR5 – volume: 55 start-page: 32 year: 2016 ident: CR10 article-title: Optimal decay of extremal functions for the fractional Sobolev inequality publication-title: Calc. Var. Partial Differ. Equations doi: 10.1007/s00526-016-0958-y contributor: fullname: Squassina – volume: 36 start-page: 683 year: 2016 end-page: 699 ident: CR17 article-title: Existence of solutions for a class of -Laplacian type equation with critical growth and potential vanishing at infinity publication-title: Discrete Cont. Dyna. Syst. contributor: fullname: Shuai – volume: 14 start-page: 14:80 year: 2017 ident: CR29 article-title: Existence of positive solutions for a class of critical fractional Schrödinger equations with potential vanishing at infinity publication-title: Mediter. J. Math. contributor: fullname: Wu – year: 1990 ident: CR37 publication-title: Hardy-Type Inequalities contributor: fullname: Kufner – volume: 5 start-page: 373 year: 2014 end-page: 386 ident: CR24 article-title: Fractional -eigenvalues publication-title: Riv. Math. Univ. Parma (N.S.) contributor: fullname: Palatucci – volume: 9 start-page: 101 year: 2014 ident: 1090_CR26 publication-title: Adv. Calc. Var. doi: 10.1515/acv-2014-0024 contributor: fullname: A Iannizzotto – volume: 28 start-page: 469 year: 2010 ident: 1090_CR34 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2010.28.469 contributor: fullname: C Mercuri – volume: 32 start-page: 1245 year: 2007 ident: 1090_CR14 publication-title: Comm. Partial Differential Equations doi: 10.1080/03605300600987306 contributor: fullname: L Caffarelli – volume: 55 start-page: 32 year: 2016 ident: 1090_CR10 publication-title: Calc. Var. Partial Differ. Equations doi: 10.1007/s00526-016-0958-y contributor: fullname: L Brasco – start-page: 162 volume-title: Variational Methods for Nonlocal Fractional Problems year: 2016 ident: 1090_CR35 doi: 10.1017/CBO9781316282397 contributor: fullname: G Molica Bisci – volume: 9 start-page: 323 year: 2016 ident: 1090_CR11 publication-title: Adv. Calc. Var. doi: 10.1515/acv-2015-0007 contributor: fullname: L Brasco – volume-title: Hardy-Type Inequalities year: 1990 ident: 1090_CR37 contributor: fullname: B Opic – volume: 55 issue: 4 year: 2016 ident: 1090_CR36 publication-title: Calc. Var. Partial Differential Equations – ident: 1090_CR40 doi: 10.1007/978-1-4612-4146-1 – volume: 31 start-page: 1161 year: 1990 ident: 1090_CR41 publication-title: Sci. Sinica. contributor: fullname: X Zhu – volume: 136 start-page: 521 year: 2012 ident: 1090_CR20 publication-title: Bull. Sci. Math. doi: 10.1016/j.bulsci.2011.12.004 contributor: fullname: E Nezza – volume: 142 start-page: 1237 year: 2012 ident: 1090_CR23 publication-title: Proc. Roy. Soc. Edinburgh Sect. A doi: 10.1017/S0308210511000746 contributor: fullname: P Felmer – volume: 267 start-page: 1807 year: 2014 ident: 1090_CR16 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2014.05.023 contributor: fullname: A Di Castro – volume: 23 issue: 5 year: 2016 ident: 1090_CR30 publication-title: Nonlinear Diff. Equat. Appl. – ident: 1090_CR5 – volume: 54 start-page: 1121 year: 2003 ident: 1090_CR18 publication-title: Nonlin. Analysis, TMA. doi: 10.1016/S0362-546X(03)00129-9 contributor: fullname: Y Deng – volume: 36 start-page: 683 year: 2016 ident: 1090_CR17 publication-title: Discrete Cont. Dyna. Syst. contributor: fullname: Y Deng – volume: 14 start-page: 14:80 year: 2017 ident: 1090_CR29 publication-title: Mediter. J. Math. doi: 10.1007/s00009-017-0846-51660-5446/17/020001-14 contributor: fullname: Q Li – volume: 32 start-page: 1353 year: 2016 ident: 1090_CR25 publication-title: Rev. Mat. Iberoam. doi: 10.4171/RMI/921 contributor: fullname: A Iannizzotto – volume: 16 start-page: 99 year: 2017 ident: 1090_CR38 publication-title: Commun. Pure Appl. Anal. doi: 10.3934/cpaa.2017004 contributor: fullname: CE Torres – volume: 43 start-page: 270 year: 1992 ident: 1090_CR39 publication-title: Z. Angew. Math. Phys. doi: 10.1007/BF00946631 contributor: fullname: P Rabinowitz – volume: 88 start-page: 486 year: 1983 ident: 1090_CR12 publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1983-0699419-3 contributor: fullname: H Brezis – volume: 5 start-page: 373 year: 2014 ident: 1090_CR24 publication-title: Riv. Math. Univ. Parma (N.S.) contributor: fullname: G Franzina – volume: 18 start-page: 1321 year: 2005 ident: 1090_CR4 publication-title: Diff. Integ. Eqns. contributor: fullname: A Ambrosetti – volume: 33 start-page: 1279 year: 2016 ident: 1090_CR15 publication-title: Ann. Inst. H. Poincaré Anal. Non Linéaire doi: 10.1016/j.anihpc.2015.04.003 contributor: fullname: A D Castro – volume: 14 start-page: 64 year: 1994 ident: 1090_CR28 publication-title: Acta Math. Sci. doi: 10.1016/S0252-9602(18)30091-2 contributor: fullname: G Li – volume: 49 start-page: 795 year: 2014 ident: 1090_CR31 publication-title: Calc. Var. Partial Differential Equations doi: 10.1007/s00526-013-0600-1 contributor: fullname: E Lindgren – volume: 199 start-page: 317 year: 2020 ident: 1090_CR6 publication-title: Ann. Mat. Pura Appl. doi: 10.1007/s10231-019-00880-7 contributor: fullname: V Ambrosio – volume: 153 start-page: 183 year: 2017 ident: 1090_CR21 publication-title: Manuscripta Math. doi: 10.1007/s00229-016-0878-3 contributor: fullname: S Dipierro – volume: 36 start-page: 437 year: 1983 ident: 1090_CR13 publication-title: Commun. Pure. Appl. Math. doi: 10.1002/cpa.3160360405 contributor: fullname: H Brezis – volume: 14 start-page: 349 year: 1973 ident: 1090_CR3 publication-title: J. Funct. Anal. doi: 10.1016/0022-1236(73)90051-7 contributor: fullname: A Ambrosetti – volume: 7 start-page: 117 year: 2005 ident: 1090_CR2 publication-title: J. Eur. Math. Soc. doi: 10.4171/JEMS/24 contributor: fullname: A Ambrosetti – volume: 36 start-page: 1813 year: 2016 ident: 1090_CR9 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2016.36.1813 contributor: fullname: L Brasco – volume: 189 start-page: 273 year: 2010 ident: 1090_CR8 publication-title: Annali Mat. Pura Appl. doi: 10.1007/s10231-009-0109-6 contributor: fullname: D Bonheure – volume: 18 start-page: 1550063 issue: 06 year: 2016 ident: 1090_CR22 publication-title: Commun. Contemp. Math. doi: 10.1142/S0219199715500637 contributor: fullname: JM do Ó – volume: 21 start-page: 1017 year: 2017 ident: 1090_CR32 publication-title: Taiwan. J. Math. doi: 10.11650/tjm/7947 contributor: fullname: H Luo – volume: 88 start-page: 233 year: 2014 ident: 1090_CR27 publication-title: Asymptot. Anal. TMA contributor: fullname: A Iannizzotto – volume: 254 start-page: 1977 year: 2013 ident: 1090_CR1 publication-title: J. Differential Equations doi: 10.1016/j.jde.2012.11.013 contributor: fullname: C Alves – volume: 263 start-page: 765 year: 2017 ident: 1090_CR19 publication-title: J. Differential Equations doi: 10.1016/j.jde.2017.02.051 contributor: fullname: L M Del Pezzo – volume: 38 start-page: 5835 year: 2018 ident: 1090_CR7 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2018254 contributor: fullname: V Ambrosio – volume: 95 start-page: 73 year: 2017 ident: 1090_CR33 publication-title: J. London Math. Soc. (2) doi: 10.1112/jlms.12009 contributor: fullname: J Mawhin |
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| Snippet | In this paper, we study the existence of positive solution for the
p
-Laplacian equations with fractional critical nonlinearity
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|... In this paper, we study the existence of positive solution for the p-Laplacian equations with fractional critical nonlinearity... |
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| SubjectTerms | Applications of Mathematics Continuity (mathematics) Laplace equation Math Applications in Computer Science Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical |
| Title | Positive Solutions for a Class of Fractional p-Laplacian Equation with Critical Sobolev Exponent and Decaying Potentials |
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