A class of Schrödinger elliptic equations involving supercritical exponential growth

Leuyacc Y.R.S. · Boundary Value Problems (2023) · DOI: 10.1186/s13661-023-01725-2

Resumen

This paper studies the existence of nontrivial solutions to the following class of Schrödinger equations: {−div(w(x)∇u)=f(x,u),x∈B1(0),u=0,x∈∂B1(0), where w(x) = (ln (1 / | x|)) β for some β∈ [0 , 1) , the nonlinearity f(x, s) behaves like exp(|s|21−β+h(|x|)), and h is a continuous radial function such that h(r) can be unbounded as r tends to 1. Our approach is based on a new Trudinger–Moser-type inequality for weighted Sobolev spaces and variational methods.

Instituciones: Universidad Nacional Mayor de San Marcos