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Positive solutions for a class of fractional boundary value problem with changing sign nonlinearity. (English) Zbl 1235.34027

Summary: We discuss the existence of positive solutions to the following fractional boundary value problem with changing sign nonlinearity.

D 0+ α u(t)+λf(t,u(t))=0,0<t<1,u(0)=u ' (0)=u(1)=0·

where 2<α3 is a real number, D 0+ α is the standard Riemann-Liouville derivative, λ is a positive parameter, f may change sign and may be singular at t=0,1.

MSC:
34A08Fractional differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
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