Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in \R²

2016/01/08 by Claudianor O. Alves, Daniele Cassani, Alves, Claudianor O. +5
Mathematics · #35B33 #35J20 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B33 #msc:35J20 #msc:35J60

paper · pdf · doi:10.48550/arxiv.1601.01743

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arxiv created 2016/01/08 · arxiv updated 2016/01/11

Abstract

We study the following singularly perturbed nonlocal Schrödinger equation -\vr²Δu +V(x)u =\vr^μ-2[(1)/(|x|^μ)∗ F(u)]f(u) in \R², where V(x) is a continuous real function on \R², F(s) is the primitive of f(s), 0<μ<2 and \vr is a positive parameter. Assuming that the nonlinearity f(s) has critical exponential growth in the sense of Trudinger-Moser, we establish the existence and concentration of solutions by variational methods.

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