Normalized solutions to the quasilinear Schrödinger system with p-Laplacian under the Lp-mass supercritical case

Abstract

Considering any dimension $N\ge 3$ and for given $a>0$, as well as a nonlinear term $g\left(u\right)$ exhibiting mass supercritical and Sobolev subcritical growth, we investigate the existence of normalized ground state solutions to the quasilinear Schrödinger equation with $L^p$-constraint via Nehari-Pohozaev manifold and minimizing method under appropriate assumptions of potential function $V\left(x\right)$. Moreover, we give the asymptotic behavior for the ground state energy as $a\to \infty$.