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Lions, P.L. (1982) Compactness and Topological Methods for Some Nonlinear Variational Problems of Mathematical Physics. Nonlinear Problems: Present and Future, Los Alamos 1981. North-Holland Mathematics Studies, 61, 17-34. https://doi.org/10.1016/S0304-0208(08)71038-7

has been cited by the following article:

• 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.