具有对数非线性项的 $p$-Laplacian Schrödinger-Poisson 方程规范化解的存在性

Abstract

Abstract:

This paper study the $p$-Laplacian Schrödinger-Poisson equations with logarithmic nonlinearity. By decomposing the logarithmic term, it is shown that the energy functional for this problem is of class $C^1$. By the Ekeland variational principle and truncation techniques, the existence of normalized solutions for the equation is obtained in both the $L^p$-mass subcritical and $L^p$-mass supercritical cases, and $C^{1,\alpha}$ local regularity of weak solution is obtained.

Key words: $p$-Laplacian equation, logarithmic Schr?dinger equation, normalized solutions, variational method

CLC Number:

O177.91

Mingxue Li, Chunliu Chen, Jiafeng Zhang. Existence of Normalized Solutions for the $p$-Laplacian Schrödinger-Poisson Equations with Logarithmic Nonlinearity[J].Acta mathematica scientia,Series A, 2026, 46(6): 2207-2224.

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Existence of Normalized Solutions for the $p$-Laplacian Schrödinger-Poisson Equations with Logarithmic Nonlinearity

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