Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schrödinger system

被引：0

作者：

Clapp, Monica ^{[1
]}

Saldana, Alberto ^{[3
]}

Soares, Mayra ^{[2
]}

Vicente-Benitez, Vctor A. ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Neurobiol, Blvd Juriquilla 3001, Campus Juriquilla, Juriquilla 76230, Queretaro, Mexico

[2] Univ Braslia, Dept Matemat, Campus Darci Ribeiro, BR-70910900 Braslia, Brazil

[3] Univ Nacl Autonoma Mexico, Inst Matemat, Circuito Exterior, Ciudad Univ, Coyoacan 04510, Mexico

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2024年

关键词：

Schr & ouml; dinger system; Weakly coupled; Competitive; Segregated solutions; Phase separation; Optimal partition; SIGN CHANGING SOLUTIONS; SCHRODINGER-EQUATIONS; ELLIPTIC PROBLEMS; SEPARATION;

D O I：

10.1007/s10231-024-01534-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the existence of a solution to a nonlinear competitive Schr & ouml;dinger system whose scalar potential tends to a positive constant at infinity with an appropriate rate. This solution has the property that all components are invariant under the action of a group of linear isometries and each component is obtained from the previous one by composing it with some fixed linear isometry. We call it a pinwheel solution. We describe the asymptotic behavior of the least energy pinwheel solutions when the competing parameter tends to zero and to minus infinity. In the latter case the components are segregated and give rise to an optimal pinwheel partition for the Schr & ouml;dinger equation, that is, a partition formed by invariant sets that are mutually isometric through a fixed isometry.

引用

页数：26