|
|
| |
| Variational Inclusion Systems in $\mathbb{R}^N$ |
| |
Citation： |
Zifei SHEN,Songqiang WAN.Variational Inclusion Systems in $\mathbb{R}^N$[J].Chinese Annals of Mathematics B,2011,32(4):619~630 |
| Page view： 1682
Net amount： 1171 |
Authors： |
Zifei SHEN; Songqiang WAN; |
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). |
|
|
| Abstract： |
The authors study the existence of nontrivial solutions to
$p$-Laplacian variational inclusion systems
$$
\begin{cases}
-\Delta_pu+|u|^{p-2}u\in\partial_1F(u,v),&\mbox{in }
\mathbb{R}^N, \-\Delta_pv+|v|^{p-2}v\in\partial_2F(u,v),&\mbox{in } \mathbb{R}^N,
\end{cases}
$$
where $N\geq 2,\ 2\leq p\leq N$ and $F:\mathbb{R}^2 \rightarrow
\mathbb{R}$ is a locally Lipschitz function. Under some growth
conditions on $F$, and by Mountain Pass Theorem and the principle
of symmetric criticality, the existence of such solutions is
guaranteed. |
Keywords： |
Mountain pass theorem, p-Laplacian, Principle of symmetric criticality,
Variational inclusion systems, (PS)-condition, Locally Lipschitz functions |
Classification： |
35J20, 35J25 |
|
|
Download PDF Full-Text
|
|
|
|
