Existence of positive solutions for fractional differential equation with nonlocal boundary condition
Summary: By using a fixed point theorem, existence of positive solutions for fractional differential equations with nonlocal boundary condition \[ D^\alpha_{0+} u(t) + a(t)f(t, u(t)) = 0, ~0 < t < 1, \] \[ u(0) = 0, ~u(1) = \sum^\infty_{i=1} \alpha_i u(\zeta_i) \] is considered, where \(1 < \alpha \leq 2\) is a real number, \(D^\alpha_{0+}\) is the standard Riemann-Liouville differentiation, and \(\zeta_i \in (0, 1), ~\alpha_i \in [0, \infty)\) with \(\sum^\infty_{i=1} \alpha_i \zeta^{\alpha -1}_i < 1, ~a \in C([0, 1], [0, \infty)),~ f \in C([0, 1] \times [0, \infty), [0, \infty))\).
scientific article; zbMATH DE number 6013181