A generic result for an eigenvalue problem with indefinite weight function. (Chinese. English summary) Zbl 1240.34051

Han, Xiaoling; An, Ruilian

Acta Math. Sin., Chin. Ser. 53, No. 6, 1111-1118 (2010).

Summary: This paper focuses on the structure of the solution set of indefinite-weight eigenvalue problems \[ -u''=\lambda(a(t)u+uf(t,u)),\;0<t<1,\;u(0)=u(1)=0, \] where \(\lambda \in \mathbb R\) is a parameter, \(a\in C[0,1]\) changes sign, \(f:[0,1]\times \mathbb R\to \mathbb R\) is a \(C^k\) function, \(k\geq 2\), and \(f(t, 0)=0,\;t \in [0,1]\).

MSC:

34B09	Boundary eigenvalue problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

indefinite weight; genericity; structure of solution set