Ground state solutions for a modified fractional Schrödinger equation with critical exponent

Abstract

In this paper, we study the existence of ground state solutions for the modified fractional Schrödinger equations (−Δ)αu+μu+κ[(−Δ)αu2]u=σ|u|p−1u+|u|q−2u,x∈RN, where N≥2, α∈false(0,1false), μ, σ and κ are positive parameters, 2<p+1<q≤2α∗:=2NN−2α, false(−normalΔfalse)α denotes the fractional Laplacian of order α. For the case 2<p+1<q<2α∗ and the case q=2α∗, the existence results of ground state solutions are given, respectively.

Ground states solutions for a modified fractional Schrödinger equation with a generalized Choquard nonlinearity

“…Recently, the authors in [32] studied the existence of ground state solutions for the following modified fractional Schrödinger equations…”