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Multiple positive solutions of a singular fractional differential equation with negatively perturbed term. (English) Zbl 1255.34010

Summary: Let \(D^\alpha_{0+}\) be the standard Riemann-Liouville derivative. We discuss the existence of multiple positive solutions for the following fractional differential equation with a negatively perturbed term \[ \begin{cases}-D^\alpha_{0+}u(t)=p(t)f(t,u(t))-q(t),& 0<t<1,\\ u(0)=u'(0)=u(1)=0,&{}\end{cases} \] where \(2<\alpha\leq 3\) is a real number, the perturbed term \(q:(0,1)\to[0,+\infty)\) is Lebesgue integrable and may be singular at some zero measures set of [0,1], which implies the nonlinear term may change sign.

MSC:

34A08 Fractional ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
45J05 Integro-ordinary differential equations
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