Normalized ground states to the p-Laplacian equation with general nonlinearities

In this paper, we consider the existence of ground state solutions to the following p-Laplacian equation {-Delta(p)u + lambda| u| (p-2)u = f(u) in R-N, integral(RN) | u| (p)dx = a > 0, where 1 < p < N and lambda is an element of R. Under general assumptions on the nonlinearity f, we treat two cases. Firstly, in a L-p-subcritical framework, we show the existence of ground state solutions with negative energy and zero, which is a global minimizer. Secondly, in the at least L-p-critical growth, we establish the existence of a mountain pass solution at positive energy level by exploiting a natural constraint related to the Pohozaev identity. (c) 2024 Elsevier Inc. All rights reserved.