Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems
We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian system Δx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n) has no solution (x(n),y(n)) satisfying condition 0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, where μ,ν>1 and 1/μ+1/ν=1...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/398681 |
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| _version_ | 1832554230664134656 |
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| author | Xiaoping Wang |
| author_facet | Xiaoping Wang |
| author_sort | Xiaoping Wang |
| collection | DOAJ |
| description | We give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian system Δx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n) has no solution (x(n),y(n)) satisfying condition 0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, where μ,ν>1 and 1/μ+1/ν=1 and α(n),β(n), and γ(n) are real-valued functions defined on ℤ. |
| format | Article |
| id | doaj-art-855d3770d22741b88eb7adac1fc2e7f6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-855d3770d22741b88eb7adac1fc2e7f62025-02-03T05:52:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/398681398681Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian SystemsXiaoping Wang0Department of Mathematics, Xiangnan College, Chenzhou, Hunan 423000, ChinaWe give several sufficient conditions under which the first-order nonlinear discrete Hamiltonian system Δx(n)=α(n)x(n+1)+β(n)|y(n)|μ-2y(n),Δy(n)=-γ(n)|x(n+1)|ν-2x(n+1)-α(n)y(n) has no solution (x(n),y(n)) satisfying condition 0<∑n=-∞+∞[|x(n)|ν+(1+β(n))|y(n)|μ]<+∞, where μ,ν>1 and 1/μ+1/ν=1 and α(n),β(n), and γ(n) are real-valued functions defined on ℤ.http://dx.doi.org/10.1155/2013/398681 |
| spellingShingle | Xiaoping Wang Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems Abstract and Applied Analysis |
| title | Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems |
| title_full | Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems |
| title_fullStr | Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems |
| title_full_unstemmed | Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems |
| title_short | Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems |
| title_sort | nonexistence of homoclinic solutions for a class of discrete hamiltonian systems |
| url | http://dx.doi.org/10.1155/2013/398681 |
| work_keys_str_mv | AT xiaopingwang nonexistenceofhomoclinicsolutionsforaclassofdiscretehamiltoniansystems |