On a fourth-order nonlinear Helmholtz equation

被引：7

作者：

Bonheure, Denis ^{[1
]}

Casteras, Jean-Baptiste ^{[1
]}

Mandel, Rainer ^{[2
]}

机构：

[1] Univ Libre Bruxelles, Dept Math, CP 214,Blvd Triomphe, B-1050 Brussels, Belgium

[2] Karlsruhe Inst Technol, Inst Anal, Englerstr 2, D-76131 Karlsruhe, Germany

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2019年 / 99卷 / 03期

关键词：

GLOBAL WELL-POSEDNESS; DUAL VARIATIONAL-METHODS; SCHRODINGER-EQUATION; STANDING WAVES; SCATTERING; REGULARITY; STABILITY;

D O I：

10.1112/jlms.12196

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the mixed dispersion fourth-order nonlinear Helmholtz equation Delta 2u-beta Delta u+alpha u=Gamma|u|p-2uinRN,for positive, bounded and ZN-periodic functions Gamma in the following three cases:(a)alpha<0,beta is an element of Ror(b)alpha>0,beta<-2 alpha or(c)alpha=0,beta<0.Using the dual method of Evequoz and Weth, we find solutions to this equation and establish some of their qualitative properties.

引用

页码：831 / 852

页数：22

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