GROUND STATE TRAVELLING WAVES IN INFINITE LATTICES

被引：2
|
作者：
Zhang, Luyu [1 ]
Ma, Shiwang [1 ]
机构：
[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2016年 / 36卷 / 03期
基金：
中国国家自然科学基金;
关键词：
FPU lattice; ground state wave; Nehari manifold; SOLITARY WAVES; EXISTENCE;
D O I：
10.1016/S0252-9602(16)30039-X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider FPU lattices with particles of unit mass. The dynamics of the system is described by the infinite system of second order differential equations q(n) = U'(q(n+1) - q(n)) - U'(q(n) - q(n-1)), n is an element of Z, where q(n) denotes the displacement of the n-th lattice site and U is the potential of interaction between two adjacent particles. Inspired by previous work due to Szulkin and Weth (Ground state solutions for some indefinite variational problems, J. Funct. Anal., 257 (2009), 3802-3822), we investigate the existence of solitary ground waves, i.e., nontrivial solutions with least possible energy.
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页码：782 / 790
页数：9
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