Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in R 3

Jichao Wang and Ting Yu
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Jichao Wang: College of Science, China University of Petroleum, Qingdao 266580, China
Ting Yu: College of Science, China University of Petroleum, Qingdao 266580, China

Mathematics, 2021, vol. 9, issue 5, 1-24

Abstract: In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the coefficients. Furthermore, without any restriction on the perturbed coefficient, we obtain a different concentration phenomenon. Besides, we obtain an existence result.

Keywords: Schrödinger–Poisson equation; critical growth; variational method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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