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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)+λa(t)f(u)=0,t(0,1),
u(0)=u(1)=0,

where aC[0,1] may change sign and fC(,). The proof of the main result is based on global bifurcation techniques.

MSC:
34B09Boundary eigenvalue problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
34C23Bifurcation (ODE)
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