Existence of ground state solution of Nehari-Pohožaev type for a quasilinear Schrödinger system

Abstract

This paper is concerned with the following quasilinear Schrödinger system in the entire space ${\mathbb{R}}^N$($N\ge 3$): $$\{\begin{array}{rl}& -\Delta u+A(x)u-\frac{1}{2}△(u^2)u=\frac{2\alpha }{\alpha +\beta }|u{|}^{\alpha -2}u|v{|}^{\beta },\\ & -\Delta v+Bv-\frac{1}{2}△(v^2)v=\frac{2\beta }{\alpha +\beta }|u{|}^{\alpha }|v{|}^{\beta -2}v.\end{array}$$ By establishing a suitable constraint set and studying related minimization problem, we prove the existence of ground state solution for $\alpha ,\beta >1$, $2<\alpha +\beta <\frac{4N}{N-2}$. Our results can be looked on as a generalization to results by Guo and Tang (Ground state solutions for quasilinear Schrödinger systems, J. Math. Anal. Appl. 389 (2012) 322).

arXiv admin note: substantial text overlap with arXiv:2305.14911