THE EXISTENCE OF GROUND STATE NORMALIZED SOLUTIONS FOR CHERN-SIMONS-SCHRÖDINGER SYSTEMS*

doi:10.1007/s10473-023-0620-7

Abstract

Abstract: In this paper, we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in $H^{1}(\mathbb{R}^{2})$. When the nonlinearity satisfies some general 3-superlinear conditions, we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in [L. Jeanjean, Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Anal. (1997)].

Key words: Chern-Simons-Schrödinger system;, non-constant potential, Pohožaev identity;, ground state normalized solution

CLC Number:

35A01

Yu MAO, Xingping WU, Chunlei TANG. THE EXISTENCE OF GROUND STATE NORMALIZED SOLUTIONS FOR CHERN-SIMONS-SCHRÖDINGER SYSTEMS^*[J].Acta mathematica scientia,Series B, 2023, 43(6): 2649-2661.

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THE EXISTENCE OF GROUND STATE NORMALIZED SOLUTIONS FOR CHERN-SIMONS-SCHRÖDINGER SYSTEMS^*

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