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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),

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

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