TITLE:
Multiplicity and Concentration of Solutions for Choquard Equation with Competing Potentials via Pseudo-Index Theory
AUTHORS:
Xinyu Zhao
KEYWORDS:
Choquard Equation, Pseudo-Index, Multiplicity, Concentration
JOURNAL NAME:
Open Access Library Journal,
Vol.10 No.12,
December
27,
2023
ABSTRACT: In this paper, we consider the following nonlinear Choquard equation -ε2Δw+V(x)w=ε-θ(Y1(w)+Y2(w)), where ε>0, N>2, Y1(w):=W1(x)[Iθ*(W1|w|p)]|w|p-2w, Y2(w):=W2(x)[Iθ*(W2|w|q)]|w|q-2w, Iθ is the Riesz potential with order Θ∈(0,N), and infRNWi>0, i=1,2. By imposing suitable assumptions to V(x),
Wi(x), i=1,2, we establish the multiplicity of semiclassical solutions by using pseudo-index theory and the existence of groundstate solutions by Nehari method. Moreover, the convergence and concentration of the positive groundstate solution are discussed.