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Existence of Multiple Positive Solutions for Choquard Equation with Perturbation

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  • Tao Xie
  • Lu Xiao
  • Jun Wang

Abstract

This paper is concerned with the following Choquard equation with perturbation: , , where , , and . This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation. Under some assumptions for the functions , we prove the existence of multiple positive solutions of the equation. Moreover, we also show that these results still hold for more generalized Choquard equation with perturbation.

Suggested Citation

  • Tao Xie & Lu Xiao & Jun Wang, 2015. "Existence of Multiple Positive Solutions for Choquard Equation with Perturbation," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-10, September.
    • Handle: RePEc:hin:jnlamp:760157
    DOI: 10.1155/2015/760157
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    Cited by:

    1. Zhipeng Yang & Yuanyang Yu, 2021. "Existence and concentration of solution for Schrödinger-Poisson system with local potential," Partial Differential Equations and Applications, Springer, vol. 2(4), pages 1-22, August.
    2. Xiaoyan Shi & Yulin Zhao & Haibo Chen, 2019. "Existence of Solutions for Nonhomogeneous Choquard Equations Involving p-Laplacian," Mathematics, MDPI, vol. 7(9), pages 1-17, September.
    3. Tao Wang, 2020. "Asymptotic Analysis of Multiple Solutions for Perturbed Choquard Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 135-142, March.

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