Homoclinic orbits for asymptotically linear discrete Hamiltonian systems

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• 作者：Xiaoping Wang (1)
  
  1. Department of Mathematics ; Xiangnan College ; Chenzhou ; Hunan ; 423000 ; P.R. China
  
• 关键词：39A11 ; 58E05 ; 70H05 ; homoclinic solution ; discrete Hamiltonian system ; asymptotically linear ; strongly indefinite functional
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,224 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

We study the existence of homoclinic solutions for the following second-order self-adjoint discrete Hamiltonian system: \(\triangle[p(n)\triangle u(n-1)]-L(n)u(n)+\nabla W(n, u(n))=0\) , where \(p(n)\) , \(L(n)\) , and \(W(n, x)\) are N-periodic in n, and \(\nabla W(n, x)\) is asymptotically linear in x as \(|x|\to\infty\) .