A nonhomogeneous Schrödinger equation involving nonlinearity with exponential critical growth and potential which can vanish at infinity

Santaria Leuyacc Y.R. · Results in Applied Mathematics (2023) · DOI: 10.1016/j.rinam.2022.100348

Resumen

The main purpose of this work is to study the existence of solutions for the following class of nonhomogeneous Schrödinger equations −Δu+V(x)u=f(u)+h(x),x∈R2, where V is a continuous potential which can vanish at infinity, the nonlinearity f possesses maximal growth range and h belong to the dual of a functional space. Using Ekeland variational principle and the Mountain Pass theorem, we prove that the above problem has at least two nontrivial weak solutions provided that h is sufficiently small.

Instituciones: Universidad Nacional Mayor de San Marcos