带 $L^2$-次临界一般非线性项的拟线性 Schrödinger 方程规范化解的存在性——献给李工宝教授 70 寿辰

Abstract

Abstract:

This paper studies the existence of normalized solutions for quasilinear Schrödinger equation with $L^2$-subcritical general nonlinearity. By using the compactness concentration principle, Schwartz symmetric technique and scaling method, this paper proves the existence and nonexistence of global least energy normalized solutions and the existence of local minimal normalized solutions. The main results can be viewed an extension of the results concerning about the existence of normalized solutions to the quasilinear equation with a pure power nonlinearity.

Key words: $L^2$-subcritical general nonlinearity, constrained minimization method, normalized solutions, existence, quasilinear Schrodinger equations

CLC Number:

O175.23

Hongyu Ye. The Existence of Normalized Solutions for the Quasilinear Schrödinger Equations with $L^2$-Subcritical General Nonlinearity[J].Acta mathematica scientia,Series A, 2025, 45(6): 1907-1927.

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The Existence of Normalized Solutions for the Quasilinear Schrödinger Equations with $L^2$-Subcritical General Nonlinearity

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