关键词: Green’s function, fixed point theorem in a cone, positive solution, higher-order differential equation

Abstract: Using the extension of Krasnoselskii's fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green's function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results.

Key words: Green’s function, fixed point theorem in a cone, positive solution, higher-order differential equation