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Multiple positive solutions of singular Dirichlet second-order boundary-value problems with derivative dependence. (English) Zbl 1203.34036

Summary: The existence of multiple positive solutions for the singular Dirichlet boundary-value problem

x '' +Φ(t)f(t,x(t),x ' (t))=0,0<t<1,x(0)=x(1)=0

is presented by using the fixed point index; here f may be singular at x=0.

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