Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 35, pp. 1-13.

Title: Positive solution to quasilinear Schrodinger equations via Orlicz space framework
       
Authors: Rui Sun (Lanzhou Univ., Lanzhou, China)
         Duchao Liu (Lanzhou Univ., Lanzhou, China)

Abstract:  
 This article concerns the existence of solutions for the generalized quasilinear Schrodinger
equation
$$
-\text{div}(g^2(u)\nabla u)+g(u)g'(u){|\nabla u|}^2+V(x)u=f(x,u),\quad x\in\mathbb{R}^N\,.
$$
We obtain a positive solution  by using a change of variables and a minimax theorem in
an Orlicz space framework.

Submitted April 22, 2021. Published April 29, 2022.
Math Subject Classifications: 35B38, 35D05, 35J20.
Key Words: Quasilinear Schrodinger equation; Orlicz space; change of variables.