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Zbl 1183.34007
Kaufmann, E.; Mboumi, E.
Positive solutions of a boundary value problem for a nonlinear fractional differential equation. (English)
[J] Electron. J. Qual. Theory Differ. Equ. 2008, Paper No. 3, 11 p., electronic only (2008). ISSN 1417-3875/e

Summary: We give sufficient conditions for the existence of at least one and at least three positive solutions to the nonlinear fractional boundary value problem $$\align & D^{\alpha}u + a(t) f(u) = 0, \quad 0<t<1,\quad 1<\alpha\leq 2,\\ & u(0) = 0,\ u'(1)= 0,\endalign$$ where $ D^{\alpha}$ is the Riemann-Liouville differential operator of order $\alpha , f: [0,\infty)\to [0,\infty)$ is a given continuous function and $a$ is a positive and continuous function on $[0,1]$.

MSC 2000:: *34A08
34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE

Keywords: fractional derivative; nonlinear dynamic equation; positive solution

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