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 − 2 Δ u + V (x) u = u log u 2 , in ℝ N , u ∈ H 1 (ℝ N) , (P ) where V : ℝ N → ℝ is a continuous function that satisfies some technical conditions and is a positive parameter. We will establish the multiplicity of solution for (P ) by using the notion of Lusternik–Schnirelmann category, by introducing a new function space where the energy functional is C 1 . [ABSTRACT FROM AUTHOR]