不定权特征值问题的一个通有性结果

A Generic Result for an Eigenvalue Problem with Indefinite Weight Function

本文应用通有性理论,讨论不定权特征值问题-u″=λ(a(t)u+uf(t,u)),0<t<1,u(0)=u(1)=0的解集结构.这里λ∈R是参数,a∈C[0,1]变号,f:[0,1]×R→R是C^k函数,k≥2,且f(t,0)=0,t∈[0,1].

By using generic theory,this paper focuses on the structure of the solutionset of indefinite weight eigenvalue problems -u″=λ（a（t）u ＋ uf（t,u））,0t1,u（0） = u（1）=0,whereλ∈R is a parameter,a∈C[0,1]changes sign,f：[0,1]×R→R is C^k function,k≥2,and f（t,0） = 0,t∈[0,1].