一类非线性p-Laplace方程正规化解的存在性

doi:10.16088/j.issn.1001-6600.2024041206

Abstract

Abstract: The existence of positive normalized solutions for a class of Schrdinger equations with a perturbation for the mass supercritical case (that is, p+p²/N*) is discussed. Firstly, by constructing an appropriate auxiliary function, it is proved that the energy functional possesses a mountain-pass geometrical structure on the constraint space. Then, the existence of a mountain pass solution with positive energy is established when h_W^1,p is sufficiently small.

Key words: p-Laplace equation, mountain-pass theorem, Palais-Smale condition, normalized solution, Pohozaev manifold

CLC Number: O175.29

GUO Xinxin, ZHONG Yansheng. Existence of Normalized Solutions for a Class of Nonlinear p-Laplace Equations[J].Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(3): 106-112.

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Existence of Normalized Solutions for a Class of Nonlinear p-Laplace Equations

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