Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8054356 | Applied Mathematics Letters | 2017 | 7 Pages |
Abstract
We consider the following singularly perturbed Schrödinger equation âε2Îu+V(x)u=f(u),uâH1(RN), where Nâ¥3, V is a nonnegative continuous potential and the nonlinear term f is of critical growth. In this paper, with the help of a truncation approach, we prove that if V has a positive local minimum, then for small ε the problem admits positive solutions which concentrate at an isolated component of positive local minimum points of V as εâ0. In particular, the potential V is allowed to be either compactly supported or decay faster than â£xâ£â2 at infinity. Moreover, a general nonlinearity f is involved, i.e., the monotonicity of f(s)/s and the Ambrosetti-Rabinowitz condition are not required.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Jianjun Zhang,