[Existence of multiple solutions for a Schröndiger logarithmic equation

2023/08/23 by Alves, Claudianor O., da Silva, Ismael S.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.12225

Abstract

This paper concerns the existence of multiple solutions for a Schrödinger logarithmic equation of the form \\beginaligned -ε²Δu + V(x)u amp; =ulog u², in ℝ^N,u ∈ H¹(ℝ^N), \endaligned .\leqno(P_ε) where V:ℝ^N\longrightarrow ℝ is a continuous function that satisfies some technical conditions and ε is a positive parameter. We will establish the multiplicity of solution for (P_ε) by using the notion of Lusternik-Schnirelmann category, by introducing a new function space where the energy functional is C¹.

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