Normalized solutions to <i>p</i>-Laplacian equations with a potential term and mass-supercritical nonlinearities

Yanfeng Li; Xuejiao Liu; Haicheng Liu; Yanfeng Li; Xuejiao Liu; Haicheng Liu

doi:10.3934/era.2026185

Electronic Research Archive

2026, Volume 34, Issue 6: 4131-4157. doi: 10.3934/era.2026185

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Research article

Normalized solutions to p-Laplacian equations with a potential term and mass-supercritical nonlinearities

College of Science, Heilongjiang Institute of Technology, Harbin 150001, China

Received: 25 March 2026 Revised: 30 April 2026 Accepted: 07 May 2026 Published: 18 May 2026

In this paper, we investigate the existence of normalized ground state solutions for a class of quasilinear elliptic equations. More precisely, we consider the p-Laplace equation with a prescribed $ L^p $-norm constraint. The problem involves a potential function and a nonlinear term with mass supercritical growth. By employing variational methods, we aim to find solutions with a given mass, where the parameter $ \lambda $ appears as a Lagrange multiplier. Under appropriate assumptions of potential and nonlinearity, we establish the existence of such solutions for any given positive mass.
- normalized solutions,
- general nonlinearities,
- mass supercritical,
- non-trapping potential
Citation: Yanfeng Li, Xuejiao Liu, Haicheng Liu. Normalized solutions to p-Laplacian equations with a potential term and mass-supercritical nonlinearities[J]. Electronic Research Archive, 2026, 34(6): 4131-4157. doi: 10.3934/era.2026185

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Abstract

In this paper, we investigate the existence of normalized ground state solutions for a class of quasilinear elliptic equations. More precisely, we consider the p-Laplace equation with a prescribed $ L^p $-norm constraint. The problem involves a potential function and a nonlinear term with mass supercritical growth. By employing variational methods, we aim to find solutions with a given mass, where the parameter $ \lambda $ appears as a Lagrange multiplier. Under appropriate assumptions of potential and nonlinearity, we establish the existence of such solutions for any given positive mass.

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