Monotone Positive Solutions for Singular Third-Order m-Point Boundary Value Problems

To investigate the existence results of single and multiple monotone positive solutions for a class of nonlinear singular m-point boundary value problems of third-order differential equations with a positive parameter. Firstly, Green's function for the associated linear boundary value problem is constructed, and then, some useful properties of the Green's function are obtained. Finally, To establish intervals of the parameter which yield the existence of at least one, two and infinitely many monotone positive solutions under suitable conditions for the above problem. The main tool is the well-known Guo-Krasnoselskii's fixed point theorem.