Mountain pass solutions to a generalized Frenkel-Kontorova model  

作　　者：Wen-Long Li 

机构地区：[1]School of Mathematics,Sun Yat-Sen University,Guangzhou 510275,China

出　　处：《Science China Mathematics》2022年第6期1293-1318,共26页中国科学：数学（英文版）

基　　金：supported by the Fundamental Research Funds for the Central Universities(Grant No.34000-31610274)。

摘　　要：We study a generalized Frenkel-Kontorova model and obtain periodic and heteroclinic mountain pass solutions.The heteroclinic mountain pass solution in the second laminations is new to the generalized Frenkel-Kontorova model.Our proof follows that of Bolotin and Rabinowitz(2005)for an Allen-Cahn equation,which is different from the heat flow method of finding the critical point of the Frenkel-Kontorova model in the literature.The proofs depend on suitable choices of functionals and working spaces.We also study the multiplicity of these mountain pass solutions.

关 键 词：mountain pass solution periodic solution heteroclinic solution Frenkel-Kontorova model 

分 类 号：O175[理学—数学]