Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems
We give several sufficient conditions under which the first-order nonlinear Hamiltonian system x'(t)=α(t)x(t)+f(t,y(t)), y'(t)=-g(t,x(t))-α(t)y(t) has no solution (x(t),y(t)) satisfying condition 0<∫-∞+∞[|x(t)|ν+(1+β(t))|y(t)|μ]dt<+∞, where μ,ν>1 and (1/μ)+(1/ν)=1, 0≤xf(t,x)≤β(t...
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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/10.1155/2013/547682 |
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| _version_ | 1832546615272931328 |
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| author | Xiaoyan Lin Qi-Ming Zhang X. H. Tang |
| author_facet | Xiaoyan Lin Qi-Ming Zhang X. H. Tang |
| author_sort | Xiaoyan Lin |
| collection | DOAJ |
| description | We give several sufficient conditions under which the first-order nonlinear Hamiltonian system x'(t)=α(t)x(t)+f(t,y(t)), y'(t)=-g(t,x(t))-α(t)y(t) has no solution (x(t),y(t)) satisfying condition 0<∫-∞+∞[|x(t)|ν+(1+β(t))|y(t)|μ]dt<+∞, where μ,ν>1 and (1/μ)+(1/ν)=1, 0≤xf(t,x)≤β(t)|x|μ, xg(t,x)≤γ0(t)|x|ν, β(t),γ0(t)≥0, and α(t) are locally Lebesgue integrable real-valued functions defined on ℝ. |
| format | Article |
| id | doaj-art-9b1c6632d01b4beea17c5f9259ca492b |
| 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-9b1c6632d01b4beea17c5f9259ca492b2025-02-03T06:47:53ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/547682547682Nonexistence of Homoclinic Orbits for a Class of Hamiltonian SystemsXiaoyan Lin0Qi-Ming Zhang1X. H. Tang2Department of Mathematics, Huaihua College, Huaihua, Hunan 418008, ChinaCollege of Science, Hunan University of Technology, Zhuzhou, Hunan 412007, ChinaSchool of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, ChinaWe give several sufficient conditions under which the first-order nonlinear Hamiltonian system x'(t)=α(t)x(t)+f(t,y(t)), y'(t)=-g(t,x(t))-α(t)y(t) has no solution (x(t),y(t)) satisfying condition 0<∫-∞+∞[|x(t)|ν+(1+β(t))|y(t)|μ]dt<+∞, where μ,ν>1 and (1/μ)+(1/ν)=1, 0≤xf(t,x)≤β(t)|x|μ, xg(t,x)≤γ0(t)|x|ν, β(t),γ0(t)≥0, and α(t) are locally Lebesgue integrable real-valued functions defined on ℝ.http://dx.doi.org/10.1155/2013/547682 |
| spellingShingle | Xiaoyan Lin Qi-Ming Zhang X. H. Tang Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems Abstract and Applied Analysis |
| title | Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems |
| title_full | Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems |
| title_fullStr | Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems |
| title_full_unstemmed | Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems |
| title_short | Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems |
| title_sort | nonexistence of homoclinic orbits for a class of hamiltonian systems |
| url | http://dx.doi.org/10.1155/2013/547682 |
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