Radial and non-radial multiple solutions to a general mixed dispersion NLS equation

被引：1

作者：

d'Avenia, Pietro ^{[1
]}

Pomponio, Alessio ^{[1
]}

Schino, Jacopo ^{[2
,3
]}

机构：

[1] Politecn Bari, Dipartimento Matemat Meccan & Management, Via Orabona 4, I-70125 Bari, Italy

[2] North Carolina State Univ, Dept Math, 2311 Stinson Dr, Raleigh, NC 27607 USA

[3] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland

来源：

NONLINEARITY | 2023年 / 36卷 / 03期

关键词：

Bilaplacian; mixed-dispersion Schrodinger equation; standing wave solutions; multiple solutions; positive mass case; zero mass case; radial and non-radial solutions; SCALAR FIELD-EQUATIONS; NONLINEAR SCHRODINGER-EQUATION; 4TH-ORDER ELLIPTIC-EQUATIONS; NORMALIZED SOLUTIONS; NONTRIVIAL SOLUTIONS; ORDER DISPERSION; EXISTENCE; COMPACTNESS; WAVES;

D O I：

10.1088/1361-6544/acb62d

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the following nonlinear Schrodinger equation with a fourth-order dispersion term?(2)u - beta?u = g(u) in R(N)in the positive and zero mass regimes: in the former, N >= 2 and beta > -2 root m, where m > 0 depends on g; in the latter, N >= 3 and beta > 0. In either regimes, we find an infinite sequence of solutions under rather generic assumptions about g; if N = 2 in the positive mass case, or N =4 in the zero mass case, we need to strengthen such assumptions. Our approach is variational.

引用

页码：1743 / 1775

页数：33

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