%0 Journal Article
%T Multiplicity and Concentration of Solutions for Choquard Equation with Competing Potentials via Pseudo-Index Theory
%A Xinyu Zhao
%J Open Access Library Journal
%V 10
%N 12
%P 1-22
%@ 2333-9721
%D 2023
%I Open Access Library
%R 10.4236/oalib.1111026
%X 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.
%K Choquard Equation
%K Pseudo-Index
%K Multiplicity
%K Concentration
%U http://www.oalib.com/paper/6811234