Sign-changing multi-bump solutions for Choquard equation with deepening potential well - Yang, Xiaolong (Topological Methods in Nonlinear Analysis, 2022)
In this paper, we are concerned with the existence of sign-changing multi-bump solutions for the following nonlinear Choquard equation equationeq0.1 -Δ u+(λ V(x)+1)u=(I_α*|u|^p)|u|^p-2u in R^N, equation where I_α is the Riesz potential, λ R^+, (N-4)^+< α< N, 2p < (N+α)/(N-2), and V(x) is a nonnegative continuous function with a potential well Ω:= int(V^-1(0)) which possesses k disjoint bounded components Ω_1, …, Ω_k. We prove the existence of sign-changing multi-bump solutions for eq0.1 if λ is large enough.