TITLE:
Existence and Concentration of Sign-Changing Solutions of Quasilinear Choquard Equation
AUTHORS:
Die Wang, Yuqi Wang, Shaoxiong Chen
KEYWORDS:
Quasilinear Choquard Equation, The Method of Invariant Sets of Descending Flow, Truncation, Sign-Changing Solutions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.4,
April
28,
2023
ABSTRACT: In this paper, we study the following quasilinear equation of choquard type:
where A(x,t) is given real functions on RN × R and with N ≥ 3, 1 p N, max{N-2p,1} α N, , and ε > 0 is a small parameter, Iα is the Riesz potential. We establish for small ε the existence of a sequence of sign-changing solutions concentrating near a given local minimum point of the bounded potential function V by using the method of invariant sets of descending flow, perturbation method and truncation technique.