Concentrating solutions for a magnetic Schrodinger equation with critical growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:479

Article

Ambrosio, Vincenzo¹ 

[1] Univ Politecn Marche, Dipartimento Ingn Ind & Sci Matemat, Via Brecce Bianche 12, I-60131 Ancona, Italy

关键词: Magnetic Laplacian;    Variational methods;    Critical growth;   

DOI  :  10.1016/j.jmaa.2019.06.070

来源: Elsevier

【 摘 要 】

We deal with the following nonlinear Schrodinger equation with magnetic field and critical growth: {epsilon/iota del - A(x)(2) u + V(x)u = f(vertical bar u vertical bar(2))u + vertical bar u vertical bar(2)*(-2) u in R-N, u is an element of H-1 (R-N, C), where epsilon > 0 is a small parameter, N >= 3, 2* = 2N/N-2 is the critical Sobolev exponent, A is an element of C-1 (R-N, R-N) is a magnetic vector potential, V : R-N -> R is a continuous positive potential having a local minimum and f : R -> R is a superlinear continuous function with subcritical growth. Using penalization techniques and variational methods, we investigate the existence and concentration of nontrivial solutions for epsilon > 0 small enough. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free