Superlinear singular fractional boundary-value problems

Abstract

In this article, we study the superlinear fractional boundary-value problem $$\displaylines{ D^{\alpha }u(x) =u(x)g(x,u(x)),\quad 00$. The function $g(x,u)\in C((0,1)\times [ 0,\infty ),[0,\infty))$ that may be singular at x=0 and x=1 is required to satisfy convenient hypotheses to be stated later.

Keywords

• Fractional differential equation
• positive solution
• Green's function
• perturbation arguments