Normalized solutions for (p,q)-Laplacian equations with mass supercritical growth

In this paper, we study the following (p,q)-Laplacian equation with Lp-constraint:{−Δpu−Δqu+λ|u|p−2u=f(u),inRN,∫RN|u|pdx=cp,u∈W1,p(RN)∩W1,q(RN), where 10 is a constant. The nonlinearity f is assumed to be continuous and satisfying weak mass supercritical conditions. The purpose of this paper is twofold: to establish the existence of ground states, and to reveal the basic behavior of the ground state energy Ec as c>0 varies. Moreover, we introduce a new approach based on the direct minimization of the energy functional on the linear combination of Nehari and Pohozaev constraints intersected with the closed ball of radius cp in Lp(RN). The analysis developed in this paper allows to provide the general growth assumptions imposed to the reaction f.