Existence of nonnegative solutions for a fractional m-point boundary value problem at resonance
1 Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong, 521041, China
2 Department of Basic Education, Hanshan Normal University, Chaozhou, Guangdong, 521041, China
Boundary Value Problems 2013, 2013:127 doi:10.1186/1687-2770-2013-127Published: 16 May 2013
We consider the fractional differential equation
satisfying the boundary conditions
where is the Riemann-Liouville fractional order derivative. The parameters in the multi-point boundary conditions are such that the corresponding differential operator is a Fredholm map of index zero. As a result, the minimal and maximal nonnegative solutions for the problem are obtained by using a fixed point theorem of increasing operators.
MSC: 26A33, 34A08.