Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ = λ ) ± ) under Robin boundary condition in a regular open bounded domain Ω of ℝ , ≥ 2. Δ is the )-Laplacian operator where ∈ ) and > 1. Our proofs are based on the sub solutio...
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| Published in | Mathematica Slovaca Vol. 72; no. 6; pp. 1541 - 1550 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
De Gruyter
16.12.2022
Walter de Gruyter GmbH |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ
= λ
)
±
)
under Robin boundary condition in a regular open bounded domain Ω of ℝ
,
≥ 2. Δ
is the
)-Laplacian operator where
∈
) and
> 1. Our proofs are based on the sub solution-super solution method and also on variational arguments. |
|---|---|
| AbstractList | Abstract
In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ
p
(
x
)
u
= λ
k
(
x
)
u
q
±
h
(
x
)
u
r
under Robin boundary condition in a regular open bounded domain Ω of ℝ
N
,
N
≥ 2. Δ
p
(
x
)
is the
p
(
x
)-Laplacian operator where
p
∈
C
1
(
Ω
) and
p
> 1. Our proofs are based on the sub solution-super solution method and also on variational arguments. In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δp(x) u = λ k(x) uq ± h(x) ur under Robin boundary condition in a regular open bounded domain Ω of ℝN, N ≥ 2. Δp(x) is the p(x)-Laplacian operator where p ∈ C1(Ω) and p > 1. Our proofs are based on the sub solution-super solution method and also on variational arguments. In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ = λ ) ± ) under Robin boundary condition in a regular open bounded domain Ω of ℝ , ≥ 2. Δ is the )-Laplacian operator where ∈ ) and > 1. Our proofs are based on the sub solution-super solution method and also on variational arguments. |
| Author | Dammak, Makkia Ali, Abir Amor Ben |
| Author_xml | – sequence: 1 givenname: Makkia surname: Dammak fullname: Dammak, Makkia email: makkia.dammak@gmail.com organization: Department of Mathematics Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia – sequence: 2 givenname: Abir Amor Ben surname: Ali fullname: Ali, Abir Amor Ben email: abir.amorbenali@gmail.com organization: Department of Mathematics Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis, Tunisia |
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| Snippet | In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ
= λ
)
±
)
under Robin boundary... Abstract In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δ p ( x ) u = λ k ( x ) u q ± h... In the present paper, we study the existence as well as the non-existence of some positive solutions for the equation −Δp(x) u = λ k(x) uq ± h(x) ur under... |
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| SubjectTerms | 35J60 35J70 35K57 Boundary conditions Coercivity generalised Sobolev spaces Laplace operator Primary 35J20 quasilinear equation sub solution-super solution method variational methods |
| Title | Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions |
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