Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian

Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian

By establishing a new proper variational framework and using the critical point theory, we establish some new existence criteria to guarantee that the 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian Δn(r(t−n)φp(Δnu(t−1)))+q(t)φp(u(t))=f(t,u(t+n),…,u(...

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Main Author: Xiaofei He
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/297618
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spelling doaj-6de97e07926246cb9c104aeeff0345062020-11-24T20:54:58ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/297618297618Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-LaplacianXiaofei He0Department of Mathematics and Computer Science, Jishou University, Hunan, Jishou 416000, ChinaBy establishing a new proper variational framework and using the critical point theory, we establish some new existence criteria to guarantee that the 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian Δn(r(t−n)φp(Δnu(t−1)))+q(t)φp(u(t))=f(t,u(t+n),…,u(t),…,u(t−n)), n∈ℤ(3), t∈ℤ, has infinitely many homoclinic orbits, where φp(s) is p-Laplacian operator; φp(s)=|s|p−2s(1<p<∞)r, q, f are nonperiodic in t. Our conditions on the potential are rather relaxed, and some existing results in the literature are improved.http://dx.doi.org/10.1155/2012/297618
collection DOAJ
language English
format Article
sources DOAJ
author Xiaofei He
spellingShingle Xiaofei He
Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian
Abstract and Applied Analysis
author_facet Xiaofei He
author_sort Xiaofei He
title Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian
title_short Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian
title_full Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian
title_fullStr Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian
title_full_unstemmed Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian
title_sort infinitely many homoclinic orbits for 2nth-order nonlinear functional difference equations involving the p-laplacian
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description By establishing a new proper variational framework and using the critical point theory, we establish some new existence criteria to guarantee that the 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian Δn(r(t−n)φp(Δnu(t−1)))+q(t)φp(u(t))=f(t,u(t+n),…,u(t),…,u(t−n)), n∈ℤ(3), t∈ℤ, has infinitely many homoclinic orbits, where φp(s) is p-Laplacian operator; φp(s)=|s|p−2s(1<p<∞)r, q, f are nonperiodic in t. Our conditions on the potential are rather relaxed, and some existing results in the literature are improved.
url http://dx.doi.org/10.1155/2012/297618
work_keys_str_mv AT xiaofeihe infinitelymanyhomoclinicorbitsfor2nthordernonlinearfunctionaldifferenceequationsinvolvingtheplaplacian
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