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

Author

Listed:
  • Jichao Wang

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Ting Yu

    (College of Science, China University of Petroleum, Qingdao 266580, China)

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.

Suggested Citation

  • Jichao Wang & Ting Yu, 2021. "Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in R 3," Mathematics, MDPI, vol. 9(5), pages 1-24, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:464-:d:505186
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