Positive solutions of a boundary value problem for a nonlinear fractional differential equation

E. Kaufmann, University of Arkansas at Little Rock, Little Rock, USA
E. Mboumi, University of Arkansas at Little Rock, Little Rock, USA

E. J. Qualitative Theory of Diff. Equ., No. 3. (2008), pp. 1-11.

Abstract: In this paper we give sufficient conditions for the existence of at least one and at least three positive solutions to the nonlinear fractional boundary value problem

\begin{eqnarray*}
&&D^{\alpha}u + a(t) f(u) = 0, \quad 0<t<1, 1<\alpha\leq2,\\
&&u(0) = 0 ,u'(1)= 0,
\end{eqnarray*}

where $ D^{\alpha}$ is the Riemann-Liouville differential operator of order $\alpha $, $f: [0,\infty)\rightarrow [0,\infty)$ is a given continuous function and $a$ is a positive and continuous function on $[0,1]$.

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