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Zbl 1188.34019
Ma, Ruyun; Han, Xiaoling
Existence and multiplicity of positive solutions of a nonlinear eigenvalue problem with indefinite weight function.
(English)
[J] Appl. Math. Comput. 215, No. 3, 1077-1083 (2009). ISSN 0096-3003

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 $f\in C(\Bbb R, \Bbb R)$. The proof of the main result is based on global bifurcation techniques.
[Mirosława Zima (Rzeszow)]
MSC 2000:
*34B09 Boundary value problems with an indefinite weight
34B18 Positive solutions of nonlinear boundary value problems
34C23 Bifurcation (periodic solutions)

Keywords: indefinite weight problem; bifurcation; positive solutions

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