文献类型：期刊文献

英文题名：Multiple Normalized Solutions to a Logarithmic Schrodinger Equation via Lusternik-Schnirelmann Category

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

机构：[1]Univ Fed Campina Grande, Unidade Academ Matemat, BR-58429 900 Campina Grande, PB, Brazil;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2024

卷号：34

期号：7

外文期刊名：JOURNAL OF GEOMETRIC ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001215482500003)】；

基金：No Statement Available

语种：英文

外文关键词：Logarithmic Schrodinger equation; Normalized solutions; Multiplicity; Lusternik-Schnirelman category; Minimization technique

摘要：In this paper we will investigate the existence of multiple normalized solutions to the logarithmic Schrodinger equation given by {-is an element of(2)Delta u + V(x)u = lambda u + u log u(2), in R-N, integral(RN )|u|(2)dx = a(2)is an element of(N), where N >= 1, a, is an element of > 0, lambda is an element of R is an unknown parameter that appears as a Lagrange multiplier and V : R-N -> (-1, +infinity) 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 C-1.