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

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.

Keywords

• Fractional differential equation
• Dirichlet problem
• positive solution
• Schauder fixed point theorem