On a fourth-order nonlinear Helmholtz equation

被引：8
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.
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页码：831 / 852
页数：22
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