We study the following singularly perturbed nonlocal Schrödinger equation. where V(. x) is a continuous real function on R2, F(s) is the primitive of f(s), 0 < μ < 2 and ε 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.
Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in R2
CASSANI, DANIELE;
2016-01-01
Abstract
We study the following singularly perturbed nonlocal Schrödinger equation. where V(. x) is a continuous real function on R2, F(s) is the primitive of f(s), 0 < μ < 2 and ε 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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