Existence of solutions for fractional $m$-point boundary-value problems at resonance with $p$-Laplacian operator
Existence of solutions for fractional $m$-point boundary-value problems at resonance with $p$-Laplacian operator
In this paper, we considered a class of $m$-point boundary-value problem of fractional differential equations at resonance with $p$-Laplacian operator in the following: \begin{eqnarray*} \left\{ \begin{array}{ll} D_{0^+}^\beta \varphi_p (D_{0^+}^\alpha u(t)) = f(t,u(t),D_{0^+}^{\alpha - 2} u(t),D_{0^+}^{\alpha - 1} u(t), D_{0^+}^\alpha u(t)),\quad t \in (0,1), \\ u(0) = u’(0)=D_{0^+}^\alpha u(0) = 0,\quad …