Electron. J. Diff. Equ., Vol. 2014 (2014), No. 50, pp. 1-7.

Positive solutions to a nonlinear fractional Dirichlet problem on the half-line

Habib Maagli, Abdelwaheb Dhifli

Abstract:
This concerns the existence of infinitely many positive solutions to the fractional differential equation
$$\displaylines{ D^{\alpha }u(x)+f(x,u,D^{\alpha -1}u)=0, \quad x>0,\cr \lim_{x\to 0^{+}}u(x)=0, }$$
where $\alpha \in (1,2]$ and f is a Borel measurable function in $\mathbb{R}^{+}\times \mathbb{R}^{+}\times \mathbb{R}^{+}$ satisfying some appropriate conditions.

Submitted November 28, 2013. Published February 19, 2014.
Math Subject Classifications: 34A08.
Key Words: Fractional differential equation; Dirichlet problem; positive solution; Schauder fixed point theorem.

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Habib Mâagli
King Abdulaziz University, Rabigh Campus
College of Sciences and Arts, Department of Mathematics
P.O. Box 344, Rabigh 21911, Saudi Arabia
email: habib.maagli@fst.rnu.tn
  Abdelwaheb Dhifli
Département de Mathématiques
Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: dhifli_waheb@yahoo.fr

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