Existence of multiple solutions for a Schrödinger logarithmic equation via Lusternik–Schnirelmann category

This paper concerns the existence of multiple solutions for a Schrödinger logarithmic equation of the form [Formula: see text] where [Formula: see text] is a continuous function that satisfies some technical conditions and [Formula: see text] is a positive parameter. We will establish the multiplicity of solution for [Formula: see text] by using the notion of Lusternik–Schnirelmann category, by introducing a new function space where the energy functional is [Formula: see text].