On a Class of Infinite-Dimensional Hamiltonian Systems with Asymptotically Periodic Nonlinearities |
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| Authors: | Minbo YANG Zifei SHEN and Yanheng DING |
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| Institution: | 1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
2. Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | The authors study the existence of homoclinic type solutions for the following system of diffusion equations on ℝ × ℝ
N
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$
\left\{ \begin{gathered}
\partial _t u - \Delta _x u + b \cdot \Delta _x u + au + V(t,x)v = H_v (t,x,u,v), \hfill \\
- \partial _t v - \Delta _x v - b \cdot \Delta _x v + av + V(t,x)u = H_u (t,x,u,v), \hfill \\
\end{gathered} \right.
$
\left\{ \begin{gathered}
\partial _t u - \Delta _x u + b \cdot \Delta _x u + au + V(t,x)v = H_v (t,x,u,v), \hfill \\
- \partial _t v - \Delta _x v - b \cdot \Delta _x v + av + V(t,x)u = H_u (t,x,u,v), \hfill \\
\end{gathered} \right.
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| Keywords: | Variational methods Least energy solution Hamiltonian system |
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