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

Abstract

In this paper, we consider the existence of ground state solutions to the following p-Laplacian equation{−Δpu+λ|u|p−2u=f(u)inRN,∫RN|u|pdx=a>0, where 1<p<N and λ∈R. Under general assumptions on the nonlinearity f, we treat two cases. Firstly, in a Lp -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 Lp-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.