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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. $$\cases D^\alpha_{0+}u(t)+\lambda f(t,u(t))=0,\ 0<t<1,\\ u(0)=u'(0)=u(1)=0.\endcases$$ where $2<\alpha\le 3$ is a real number, $D^\alpha_{0+}$ is the standard Riemann-Liouville derivative, $\lambda$ is a positive parameter, $f$ may change sign and may be singular at $t=0,1$.

MSC:
 34A08 Fractional differential equations 34B18 Positive solutions of nonlinear boundary value problems for ODE 34B16 Singular nonlinear boundary value problems for ODE
Full Text:
References:
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