Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian
By applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptotically p-linear difference system with p-Laplacian Δ(|Δu(n-1)|p-2Δu(n-1))+∇[-K(n,u(n))+W(n,u(n))]=0, where p∈(1,+∞), n∈ℤ, u∈ℝN, K,W:ℤ×ℝN→ℝ are not...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/351562 |
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doaj-0be60243b0434c5caaffa4c72ebecb6e2020-11-24T22:09:13ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/351562351562Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-LaplacianQiongfen Zhang0X. H. Tang1School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, ChinaSchool of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, ChinaBy applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptotically p-linear difference system with p-Laplacian Δ(|Δu(n-1)|p-2Δu(n-1))+∇[-K(n,u(n))+W(n,u(n))]=0, where p∈(1,+∞), n∈ℤ, u∈ℝN, K,W:ℤ×ℝN→ℝ are not periodic in n, and W is asymptotically p-linear at infinity.http://dx.doi.org/10.1155/2011/351562 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Qiongfen Zhang X. H. Tang |
| spellingShingle |
Qiongfen Zhang X. H. Tang Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian Abstract and Applied Analysis |
| author_facet |
Qiongfen Zhang X. H. Tang |
| author_sort |
Qiongfen Zhang |
| title |
Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian |
| title_short |
Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian |
| title_full |
Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian |
| title_fullStr |
Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian |
| title_full_unstemmed |
Existence of Homoclinic Orbits for a Class of Asymptotically p-Linear Difference Systems with p-Laplacian |
| title_sort |
existence of homoclinic orbits for a class of asymptotically p-linear difference systems with p-laplacian |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2011-01-01 |
| description |
By applying a variant version of Mountain Pass Theorem in critical point theory, we prove the existence of homoclinic solutions for the following asymptotically p-linear difference system with p-Laplacian
Δ(|Δu(n-1)|p-2Δu(n-1))+∇[-K(n,u(n))+W(n,u(n))]=0,
where p∈(1,+∞), n∈ℤ, u∈ℝN, K,W:ℤ×ℝN→ℝ are not periodic in n,
and W is asymptotically p-linear at infinity. |
| url |
http://dx.doi.org/10.1155/2011/351562 |
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AT qiongfenzhang existenceofhomoclinicorbitsforaclassofasymptoticallyplineardifferencesystemswithplaplacian AT xhtang existenceofhomoclinicorbitsforaclassofasymptoticallyplineardifferencesystemswithplaplacian |
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