Existence and multiplicity of positive solutions of a nonlinear eigenvalue problem with indefinite weight function. (English) Zbl 1188.34019

Ma, Ruyun; Han, Xiaoling

Appl. Math. Comput. 215, No. 3, 1077-1083 (2009).

The paper deals with the existence, multiplicity and stability of positive solutions for the following boundary value problem
\[ u''(t)+\lambda a(t)f(u)=0, \;\;t\in (0,1), \]
\[ u(0)=u(1)=0, \]
where \(a\in C[0,1]\) may change sign and \(f\in C(\mathbb R, \mathbb R)\). The proof of the main result is based on global bifurcation techniques.

Reviewer: Mirosława Zima (Rzeszow)

MSC:

34B09	Boundary eigenvalue problems for ordinary differential equations
34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34C23	Bifurcation theory for ordinary differential equations

Keywords:

indefinite weight problem; bifurcation; positive solutions

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