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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
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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| _version_ | 1832565487845769216 |
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| author | Qiongfen Zhang X. H. Tang |
| author_facet | Qiongfen Zhang X. H. Tang |
| author_sort | Qiongfen Zhang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-0be60243b0434c5caaffa4c72ebecb6e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0be60243b0434c5caaffa4c72ebecb6e2025-02-03T01:07:28ZengWileyAbstract 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2011/351562 |
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