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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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/297618 |
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| author | Xiaofei He |
| author_facet | Xiaofei He |
| author_sort | Xiaofei He |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-6de97e07926246cb9c104aeeff034506 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6de97e07926246cb9c104aeeff0345062025-02-03T01:21:41ZengWileyAbstract 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 |
| spellingShingle | Xiaofei He Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian Abstract and Applied Analysis |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2012/297618 |
| work_keys_str_mv | AT xiaofeihe infinitelymanyhomoclinicorbitsfor2nthordernonlinearfunctionaldifferenceequationsinvolvingtheplaplacian |