Ground states of nonlinear fractional Schr\"odinger equation involving critical growth

TL;DR

This paper establishes the existence of ground state solutions for a nonlinear fractional Schrödinger equation with critical growth, without relying on common growth conditions, especially when the potential is non-constant and non-radial.

Contribution

It proves the existence of ground states for a class of nonlinear fractional Schrödinger equations without the Ambrosetti-Rabinowitz and monotonicity conditions, extending previous results to more general potentials.

Findings

Existence of ground state solutions under non-constant, non-radial potentials.

Solutions obtained without the Ambrosetti-Rabinowitz condition.

Addresses critical growth nonlinearities in fractional Schrödinger equations.

Abstract

In this paper, we are concerned with the ground state solutions of nonlinear fractional Schr\"odinger equation involving critical growth. Without Ambrosetti-Rabinowitz condition and monotonicity condition on the nonlinearity, we get the existence of ground state solutions of such equation when the potential $V(x)$ is not a constant and not radial.