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Existence of Positive Ground States of Nonlocal Nonlinear Schrödinger Equations

Author

Listed:
  • Yong-Chao Zhang

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Taishan Road 143, Qinhuangdao 066004, China)

  • Yao Lu

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Taishan Road 143, Qinhuangdao 066004, China)

Abstract

We investigate ground states of a (nonlocal) nonlinear Schrödinger equation which generalizes classical (fractional, relativistic, etc.) Schrödinger equations, so that we extend relevant results and study common properties of these equations in a uniform way. To obtain the existence of ground states, we first solve a minimization problem and then prove that the solution of the minimization problem is a ground state of the equation. After examining the regularity of the solutions to the equation, we demonstrate that any ground state is sign-definite.

Suggested Citation

  • Yong-Chao Zhang & Yao Lu, 2023. "Existence of Positive Ground States of Nonlocal Nonlinear Schrödinger Equations," Mathematics, MDPI, vol. 11(20), pages 1-8, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4316-:d:1261265
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