文献类型：期刊文献

英文题名：Multiple normalized solutions to a logarithmic Schr?dinger equation via Lusternik-Schnirelmann category

作者：Alves, Claudianor O.[1]; Ji, Chao[2]

机构：[1] Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, Campina Grande, PB, CEP:58429-900, Brazil; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2023

外文期刊名：arXiv

收录：EI(收录号：20230244979)

语种：英文

摘要：In this paper our objective is to investigate the existence of multiple normalized solutions to the logarithmic Schr?dinger equation given by { Z? R ? N2? |u u |2dx + V = (x a ) 2 u ?N = , λu + u log u2, in RN , where a, ? > 0, λ ∈ R is an unknown parameter that appears as a Lagrange multiplier and V: RN → [?1, ∞) is a continuous function. Our analysis demonstrates that the number of normalized solutions of the equation is associated with the topology of the set where the potential function V attains its minimum value. To prove the main result, we employ minimization techniques and use the Lusternik-Schnirelmann category. Additionally, we introduce a new function space where the energy functional associated with the problem is of class C1 ? 2023, CC BY.