On nulls of perturbed Fredholm operators and degenerate homoclinic bifurcations  

作　　者：ZHANG WeinianDepartment of Mathematics, Sichuan University, Chengdu 610064, China 

出　　处：《Science China Mathematics》2004年第4期617-627,共11页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10171071);China MOE Research Grants TRAPOYT.

摘　　要：It is known that small perturbations of a Fredholm operatorL have nulls of dimension not larger than dimN(L). In this paper for any given positive integer κ ? dimN(L) we prove that there is a perturbation ofL which has an exactly κ-dimensional null. Actually, our proof gives a construction of the perturbation. We further apply our result to concrete examples of differential equations with degenerate homoclinic orbits, showing how many independent homoclinic orbits can be bifurcated from a perturbation.It is known that small perturbations of a Fredholm operator L have nulls of dimension not larger than dirnN(L). In this paper for any given positive integer κ≤ dimN(L)we prove that there is a perturbation of L which has an exactlyκ-dimensional null. Actually,our proof gives a construction of the perturbation. We further apply our result to concrete examples of differential equations with degenerate homoclinic orbits, showing how many independent homoclinic orbits can be bifurcated from a perturbation.

关 键 词：FREDHOLM operator  perturbation  dimension  decomposition  DEGENERATE HOMOCLINIC bifurcation. 

分 类 号：O177[理学—数学]