带有规范场的非线性 Schrödinger 方程在不定位势下的驻波解——献给邓引斌教授 70 寿辰

Abstract

Abstract:

In this paper, we mainly study the existence of standing wave solutions for nonlinear Schrödinger equations with the Chern-Simons gauge field on the plane. Compared with most existing works in the literature, the main novelty of this paper lies in allowing the sign of the Schrödinger operator $-\Delta+V$ to be indefinite, so that the corresponding variational functional does not satisfy the mountain pass geometry. By using a local linking technique and the infinite-dimensional Morse theory, we obtain a nontrivial solution to the problem. Moreover, under the assumption that the nonlinearity is odd, we establish the existence of infinitely many high-energy solutions via the fountain theorem.

Key words: Chern-Simons gauge field, indefinite potential, standing waves, critical groups

CLC Number:

O175.23

Xuetong Ding, Wentao Huang. Standing Waves for a Gauged Nonlinear Schrödinger Equation with Indefinite Potential[J].Acta mathematica scientia,Series A, 2026, 46(4): 1360-1373.

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References 38

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Standing Waves for a Gauged Nonlinear Schrödinger Equation with Indefinite Potential

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