刘玥; 王征平
Liu Yue; Wang Zhengping
摘要:
This article considers the equation
△2 u =f(x,u)
with boundary conditions either $u|_{\partial\Omega}=\frac{\partial u}{\partial n}|_{\partial\Omega}=0 $ or $u|_{\partial\Omega}=\bigtriangleup
u|_{\partial\Omega}=0$, where $f(x,t)$ is asymptotically linear with respect to t at infinity, and $\Omega$ is a smooth bounded domain in RN, N >4. By a variant version of Mountain Pass Theorem, it is proved that the above problems have a nontrivial solution under suitable assumptions of f(x,t).
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