Compactness results for Schrodinger equations with asymptotically linear terms

[摘要] We study the nonlinear problem -Delta u + V(x) = f (x, u), x is an element of R-N, lim(vertical bar x vertical bar ->infinity) u(x) = 0, where the Schrodinger operator -Delta + 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. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15