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

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.

### 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
Full Text:

### References:

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