Solvability of a fractional differential equation multipoint boundary value problem at resonance in ℝn

Abstract

In this paper, the solvability of a fractional differential equation multipoint boundary value problem at resonance in is investigated by utilizing the Mawhin's continuation theorem. In order to relax the assumptions of matrices in the boundary conditions, the Moore–Penrose pseudoinverse matrix is introduced to construct projectors. Furthermore, a ternary Carathéodory function that is nondecreasing in the last two variables and exhibits at most linear growth after integrating with respect to the first variable is used as a control function to constrain the nonlinear term.