Ground state solutions for quasilinear Schrödinger equations with variable potential and superlinear reaction (Q1998672)

The authors consider a quasilinear Schrödinger equation of the form \[ -\Delta u+V(x)u-\frac{1}{2}\Delta \left(u^2\right)u=g(u),\quad x\in\mathbb{R}^N, \] where \(N \geq 3\), \(V\in C(\mathbb{R}^N,[0,\infty))\) and \(g\in C(\mathbb{R},\mathbb{R})\) is superlinear at infinity. Under very general assumptions on \(V\) and \(g\) and by using variational tools and some new analytic techniques, it is shown that the problem above admits a ground state solution, where a solution is called a ground state solution if its energy is minimal among all nontrivial solutions.