Some properties of Melnikov functions near a cuspidal loop  

作　　者：Junmin Yang Maoan Han 

机构地区：[1]School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China [2]Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Science China Mathematics》2024年第4期767-786,共20页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11971145);supported by National Natural Science Foundation of China(Grant No.11931016);the National Key R&D Program of China(Grant No.2022YFA1005900)。

摘　　要：In this paper,we consider the first-order Melnikov functions and limit cycle bifurcations of a nearHamiltonian system near a cuspidal loop.By establishing relations between the coefficients in the expansions of the two Melnikov functions,we give a general method to obtain the number of limit cycles near the cuspidal loop.As an application,we consider a kind of Liénard systems and obtain a new estimation on the lower bound of the maximum number of limit cycles.

关 键 词：Melnikov function nilpotent cusp limit cycle BIFURCATION 

分 类 号：O175[理学—数学]