Author(s)

Xinyu Zhao

School of Mathematics, Liaoning Normal University, Dalian, China.

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)[I_θ*(W₁|w|^p)]|w|^p-2w, Y₂(w):=W₂(x)[I_θ*(W₂|w|^q)]|w|^q-2w, I_θ is the Riesz potential with order Θ∈(0,N),  and inf_R^NW_i>0, i=1,2. By imposing suitable assumptions to V(x), W_i(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.

Choquard Equation, Pseudo-Index, Multiplicity, Concentration

Zhao, X.Y. (2023) Multiplicity and Concentration of Solutions for Choquard Equation with Competing Potentials via Pseudo-Index Theory. Open Access Library Journal, 10, 1-22. doi: 10.4236/oalib.1111026.