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

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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 λ appears as a Lagrange multiplier. Under appropriate assumptions of potential and nonlinearity, we establish the existence of such solutions for any given positive mass.

Keywords

normalized solutions / general nonlinearities / mass supercritical / non-trapping potential

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