Existence of positive solutions of fractional differential equations with integral boundary conditions. (Chinese. English summary) Zbl 1449.34073
Summary: Based on the fixed-point index theory in a cone, by constructing a cone and the properties of the Green function, we give the existence, multiplicity and nonexistence of positive solutions for the following nonlinear boundary value problem
\[\begin{cases}
{}^CD^\alpha u (t) +\lambda f (t,u(t)) = 0, \quad t \in (0,1),\\
u (0) = u'' (0) = 0, \quad u (1) = \mu\int_0^1 u (s)\mathrm{d}s,
\end{cases}\]
with two parameters under different growth conditions, where \(2<\alpha<3\). \(0<\mu<2\) and \(\lambda>0\) are two parameters.
MSC:
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
| 34B27 | Green’s functions for ordinary differential equations |
| 34B08 | Parameter dependent boundary value problems for ordinary differential equations |
