Positive solutions for multipoint boundary value problem of fractional differential equations
The author studies the existence of positive solutions for the boundary value problem \[ \begin{cases} D^{\alpha}u(t)~+~f(t,u(t))~=~0,~~t\in (0,1) \text{~~and~~} \alpha \in(2,3),\\ u(0)~=~u^{\prime}(0)~=~0, ~~~ u^{\prime}(1)~=~\sum_{i=1}^{m-2}~a_i~u^{\prime}(\xi_i).\end{cases}\tag{*} \] He proves in Theorem 3.4 that the problem (*) has at least one positive solution. In Theorem 3.5 he shows, under some additional conditions, that the problem (*) has at least three positive solutions.
scientific article; zbMATH DE number 5848812