Solutions for fractional boundary value problem with sign-changing Green's function

摘要

In this paper, we study the solutions for the fractional boundary value problem ~cD_t~α u(t) + g(t) f (u(t)) = 0, t ∈ (0,1), u(0)=0, u(1)=0, (1), where 1 < α < 2 is a real number. Define a new cone to solve the difficulty. And investigate solutions for the problem (1) with a sign-changing Green's function. And will research the sign-changing solutions.