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Zbl 1240.34051
Han, Xiaoling; An, Ruilian
A generic result for an eigenvalue problem with indefinite weight function.
(Chinese. English summary)
[J] Acta Math. Sin., Chin. Ser. 53, No. 6, 1111-1118 (2010). ISSN 0583-1431

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 $\lambda \in \Bbb R$ is a parameter, $a\in C[0,1]$ changes sign, $f:[0,1]\times \Bbb R\to \Bbb R$ is a $C^k$ function, $k\geq 2$, and $f(t, 0)=0,\ t \in [0,1]$.
MSC 2000:
*34B09 Boundary value problems with an indefinite weight
34B15 Nonlinear boundary value problems of ODE

Keywords: indefinite weight; genericity; structure of solution set

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