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Structure of positive solution sets of semi-positone singular boundary value problems. (English) Zbl 1193.34047

The authors discuss the existence, multiplicity and the structure of positive solution sets of the following boundary value problem with integral boundary condition at an end-point:

y '' +λf(t,y)=0,0<t<1,y(0)=0,y(1)= 0 1 α(s)y(s)ds,

where λ is a positive parameter, α,f are continuous functions with the nonlinearity f satisfying some sign and growth condition but may have some space singularity at the origin. The existence results are obtained via index fixed point theory together with the Rabinowitz global bifurcation theories.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
47J15Abstract bifurcation theory