Positive solutions for generalized quasilinear Schrodinger equations

This article concerns the existence of solutions to the generalized quasilinear Schrodinger equation$$ -\text{div} (g^2(u)\nabla u)+g(u)g'(u)|\nabla u|^2+V(x)u=f(x,u), \quad x\in \mathbb{R}^N, $$ where \(N \ge 1\), \(g \in C^1(\mathbb{R})\) and the nonlinearity is asymptotically linear at infinity. Through the stretching transformation, we adjust the approach in [1]and overcome the impediment that there might not exist a \(t>0\) such that \(t u_\infty(x-y)\) belongs to the Nahari manifold, where \(u_\infty\) is a ground state solution for the limiting problem. For more information and the latesxfiles, see https://ejde.math.txstate.edu/Volumes/2026/19/abstr.html