Affiliation:
1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China
Abstract
We consider the systems of(-1)mu(2m)=λu+λv+uf(t,u,v), t∈(0,1), u(2i)(0)=u(2i)(1)=0, and0≤i≤m-1, (-1)mv(2m)=μu+μv+vg(t,u,v), t∈(0,1), v(2i)(0)=v(2i)(1)=0, 0≤i≤m-1, whereλ,μ∈Rare real parameters.f,g:[0,1]×R2→RareCk,k≥3functions andf(t,0,0)=g(t,0,0)=0,t∈[0,1]. It will be shown that if the functions,fandgare “generic” then the solution set of the systems consists of a countable collection of 2-dimensional,Ckmanifolds.
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,Analysis