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| On a Class of Infinite-Dimensional Hamiltonian Systems with Asymptotically Periodic Nonlinearities |
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Citation： |
Minbo YANG,Zifei SHEN,Yanheng DING.On a Class of Infinite-Dimensional Hamiltonian Systems with Asymptotically Periodic Nonlinearities[J].Chinese Annals of Mathematics B,2011,32(1):45~58 |
| Page view： 1825
Net amount： 1208 |
Authors： |
Minbo YANG; Zifei SHEN; Yanheng DING; |
Foundation： |
the National Natural Science Foundation of China (No. 10971194), the Zhejiang
Provincial Natural Science Foundation of China (Nos. Y7080008, R6090109) and the Zhejiang Innovation
Project (No. T200905). |
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| Abstract： |
The authors study the existence of homoclinic type solutions
for the following system of diffusion equations on $ \R\times \R^N$:
\begin{align*}
\left\{\!\!\!\begin{array}{ll}
\partial_t u-\Delta_x u+b\cdot\nabla_x u+au +V(t,x)v = H_v(t,x,u,v),
\\[1mm]
-\partial_t v-\Delta_x v-b\cdot\nabla_x v+av + V(t,x)u =
H_u(t,x,u,v),
\end{array}\right.
\end{align*}
where $z=(u,v): \R\times \R^N \to \R^m\times \R^m$, $a>0$,
$b=(b_1,\cdots,b_N)$ is a constant vector and $V\in C(\R\times
\R^N, \R)$, $H\in C^1( \R\times \R^N\times \R^{2m}, \R)$. Under
suitable conditions on $V(t,x)$ and the nonlinearity for $H(t,x,z)$,
at least one non-stationary homoclinic solution with least energy
is obtained. |
Keywords： |
Variational methods, Least energy solution, Hamiltonian system |
Classification： |
35R30, 49J40, 58D30 |
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