Compactness results for Schrödinger equations with asymptotically linear terms
Compactness results for Schrödinger equations with asymptotically linear terms
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DOI：
10.1016/j.jde.2006.05.007
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发表时间：
2006-12
影响因子：
2.4
通讯作者：
Zhaoli Liu;Jiabao Su;T. Weth
中科院分区：
文献类型：
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作者：
Zhaoli Liu;Jiabao Su;T. Weth
本文研究非线性问题−Δu+V（x）=f（x，u），x∈RN，lim| X| →∞u（x）=0，其中薛定谔算子−Δ+V是半有界的，非线性函数f是线性有界的。在一般谱理论的假设下，建立了能量泛函的Palais-Smale序列和Cerami序列的紧性.应用这些结果，当能量泛函具有山路几何时，我们得到了三个非平凡解的存在性。
We study the nonlinear problem −Δu+V(x)=f(x,u), x∈RN, lim|x|→∞u(x)=0, where the Schrödinger operator −Δ+V is semibounded and the nonlinearity f is linearly bounded. We establish compactness of Palais–Smale sequences and Cerami sequences for the associated energy functional under general spectral-theoretic assumptions. Applying these results, we obtain existence of three nontrivial solutions if the energy functional has a mountain-pass geometry.