Compactness results for Schrödinger equations with asymptotically linear terms |
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Authors: | Zhaoli Liu Jiabao Su Tobias Weth |
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Institution: | a Department of Mathematics, Capital Normal University, Beijing 100037, PR China b Mathematisches Institut, Universität Giessen, Arndtstrasse 2, 35392 Giessen, Germany |
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Abstract: | 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. |
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