On the asymptotic behavior of solutions of Emden–Fowler equations on time scales
Consider the Emden-Fowler dynamic equation where is the quotient of odd positive integers, and denotes a time scale which is unbounded above and satisfies an additional condition (C) given below. We prove that if (and when α = 1 we also assume lim t →∞ tp ( t ) μ ( t ) = 0), then (0.1) has a soluti...
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| Published in | Annali di matematica pura ed applicata Vol. 191; no. 2; pp. 205 - 217 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer-Verlag
01.05.2012
Springer Nature B.V |
| Subjects | |
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| Abstract | Consider the Emden-Fowler dynamic equation
where
is the quotient of odd positive integers, and
denotes a time scale which is unbounded above and satisfies an additional condition (C) given below. We prove that if
(and when
α
= 1 we also assume lim
t
→∞
tp
(
t
)
μ
(
t
) = 0), then (0.1) has a solution
x
(
t
) with the property that |
|---|---|
| AbstractList | Consider the Emden-Fowler dynamic equation
where
is the quotient of odd positive integers, and
denotes a time scale which is unbounded above and satisfies an additional condition (C) given below. We prove that if
(and when
α
= 1 we also assume lim
t
→∞
tp
(
t
)
μ
(
t
) = 0), then (0.1) has a solution
x
(
t
) with the property that Consider the Emden-Fowler dynamic equation where is the quotient of odd positive integers, and denotes a time scale which is unbounded above and satisfies an additional condition (C) given below. We prove that if (and when α = 1 we also assume limt→∞tp(t)μ(t) = 0), then (0.1) has a solution x(t) with the property that |
| Author | Baoguo, Jia Peterson, Allan Erbe, Lynn |
| Author_xml | – sequence: 1 givenname: Lynn surname: Erbe fullname: Erbe, Lynn email: lerbe2@math.unl.edu organization: Department of Mathematics, University of Nebraska-Lincoln – sequence: 2 givenname: Jia surname: Baoguo fullname: Baoguo, Jia organization: Department of Mathematics, University of Nebraska-Lincoln, School of Mathematics and Computer Science, Zhongshan University – sequence: 3 givenname: Allan surname: Peterson fullname: Peterson, Allan organization: Department of Mathematics, University of Nebraska-Lincoln |
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| Cites_doi | 10.1080/10236190802409312 10.1090/S0002-9947-1959-0111897-8 10.1137/0114061 10.1080/10236190802631881 10.1093/qmath/os-2.1.259 10.1016/j.aml.2008.07.014 10.1016/j.cam.2009.06.039 10.2140/pjm.1955.5.643 10.1007/978-1-4612-0201-1 |
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| Keywords | Emden-Fowler equation 39A99 39A10 34N05 Asymptotic behavior Generalized Gronwall’s Inequality 34K11 |
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| References | Baoguo, Erbe, Peterson (CR3) 2009; 232 CR6 Atkinson (CR1) 1955; 5 Wong James (CR15) 1966; 14 CR7 Bellman (CR8) 1953 Fowler (CR13) 1931; 2 Bohner, Peterson (CR9) 2001 Došlý, Řehák (CR12) 2005 Moore, Nehari (CR14) 1959; 93 Baoguo, Erbe, Peterson (CR5) 2010; 16 Baoguo, Erbe, Peterson (CR2) 2009; 22 Bohner, Peterson (CR10) 2003 Baoguo, Erbe, Peterson (CR4) 2010; 16 Erbe (CR11) 2001; 9 179_CR6 L. Erbe (179_CR11) 2001; 9 S.W. Wong James (179_CR15) 1966; 14 R.A. Moore (179_CR14) 1959; 93 179_CR7 J. Baoguo (179_CR4) 2010; 16 J. Baoguo (179_CR3) 2009; 232 J. Baoguo (179_CR5) 2010; 16 J. Baoguo (179_CR2) 2009; 22 R. Bellman (179_CR8) 1953 (179_CR10) 2003 O. Došlý (179_CR12) 2005 F.V. Atkinson (179_CR1) 1955; 5 R.H. Fowler (179_CR13) 1931; 2 M. Bohner (179_CR9) 2001 |
| References_xml | – volume: 16 start-page: 15 year: 2010 end-page: 36 ident: CR5 article-title: A Wong-type oscillation theorem for second order linear dynamic equations on time scales publication-title: J. Differ. Equs. Appl. doi: 10.1080/10236190802409312 contributor: fullname: Peterson – volume: 93 start-page: 30 year: 1959 end-page: 52 ident: CR14 article-title: Nonoscillation theorems for a class of nonlinear differential equations publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1959-0111897-8 contributor: fullname: Nehari – year: 2003 ident: CR10 publication-title: Advances in Dynamic Equations on Time Scales contributor: fullname: Peterson – volume: 14 start-page: 724 year: 1966 end-page: 728 ident: CR15 article-title: On two theorems of Waltman publication-title: SIAM J. Appl. Math. doi: 10.1137/0114061 contributor: fullname: Wong James – year: 1953 ident: CR8 publication-title: Stability Theory of Differential Equations, Dover Books on Intermediate and Advanced Mathematics contributor: fullname: Bellman – volume: 16 start-page: 217 year: 2010 end-page: 226 ident: CR4 article-title: Oscillation of sublinear Emden–Fowler dynamic equations on time scales publication-title: J. Differ. Equs. Appl. doi: 10.1080/10236190802631881 contributor: fullname: Peterson – volume: 2 start-page: 259 year: 1931 end-page: 288 ident: CR13 article-title: Further studies of Emden’s and similar differential equations publication-title: Quart. J. Math. doi: 10.1093/qmath/os-2.1.259 contributor: fullname: Fowler – year: 2005 ident: CR12 publication-title: Half-Linear Differential Equations contributor: fullname: Řehák – volume: 22 start-page: 871 year: 2009 end-page: 875 ident: CR2 article-title: Oscillation of a family of -difference equations publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2008.07.014 contributor: fullname: Peterson – year: 2001 ident: CR9 publication-title: Dynamic Equations on Time Scales: An Introduction with Applications contributor: fullname: Peterson – ident: CR6 – volume: 5 start-page: 643 year: 1955 end-page: 647 ident: CR1 article-title: On second order nonlinear oscillations publication-title: Pac. J. Math. contributor: fullname: Atkinson – ident: CR7 – volume: 232 start-page: 594 year: 2009 end-page: 599 ident: CR3 article-title: Nonoscillation for second order sublinear dynamic equations on time scales publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.06.039 contributor: fullname: Peterson – volume: 9 start-page: 346 year: 2001 end-page: 375 ident: CR11 article-title: Oscillation criteria for second order linear equations on a time scale publication-title: Canad. Appl. Math. Quart. contributor: fullname: Erbe – volume: 14 start-page: 724 year: 1966 ident: 179_CR15 publication-title: SIAM J. Appl. Math. doi: 10.1137/0114061 contributor: fullname: S.W. Wong James – volume: 16 start-page: 217 year: 2010 ident: 179_CR4 publication-title: J. Differ. Equs. Appl. doi: 10.1080/10236190802631881 contributor: fullname: J. Baoguo – volume: 5 start-page: 643 year: 1955 ident: 179_CR1 publication-title: Pac. J. Math. doi: 10.2140/pjm.1955.5.643 contributor: fullname: F.V. Atkinson – volume: 9 start-page: 346 year: 2001 ident: 179_CR11 publication-title: Canad. Appl. Math. Quart. contributor: fullname: L. Erbe – volume: 93 start-page: 30 year: 1959 ident: 179_CR14 publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-1959-0111897-8 contributor: fullname: R.A. Moore – volume: 22 start-page: 871 year: 2009 ident: 179_CR2 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2008.07.014 contributor: fullname: J. Baoguo – volume: 232 start-page: 594 year: 2009 ident: 179_CR3 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.06.039 contributor: fullname: J. Baoguo – ident: 179_CR7 – ident: 179_CR6 – volume: 16 start-page: 15 year: 2010 ident: 179_CR5 publication-title: J. Differ. Equs. Appl. doi: 10.1080/10236190802409312 contributor: fullname: J. Baoguo – volume: 2 start-page: 259 year: 1931 ident: 179_CR13 publication-title: Quart. J. Math. doi: 10.1093/qmath/os-2.1.259 contributor: fullname: R.H. Fowler – volume-title: Stability Theory of Differential Equations, Dover Books on Intermediate and Advanced Mathematics year: 1953 ident: 179_CR8 contributor: fullname: R. Bellman – volume-title: Dynamic Equations on Time Scales: An Introduction with Applications year: 2001 ident: 179_CR9 doi: 10.1007/978-1-4612-0201-1 contributor: fullname: M. Bohner – volume-title: Half-Linear Differential Equations year: 2005 ident: 179_CR12 contributor: fullname: O. Došlý – volume-title: Advances in Dynamic Equations on Time Scales year: 2003 ident: 179_CR10 |
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| Snippet | Consider the Emden-Fowler dynamic equation
where
is the quotient of odd positive integers, and
denotes a time scale which is unbounded above and satisfies an... Consider the Emden-Fowler dynamic equation where is the quotient of odd positive integers, and denotes a time scale which is unbounded above and satisfies an... |
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| SubjectTerms | Asymptotic properties Mathematics Mathematics and Statistics Quotients |
| Title | On the asymptotic behavior of solutions of Emden–Fowler equations on time scales |
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