Existence of Positive Solutions of Nonlinear Second-Order M-Point Boundary Value Problem

Introduction

The study of multi-point boundary value problems for linear second-order ordinary value problems was initialed by Llyin and Moisser (1987). Then Gupta studied three-point boundary value problems for nonlinear ordinary differential equations. We refer the reader to the reference (Gupta et al., 1994; Feng et al., 1997; Ma, 2001; Sun, 2005) for some recent results of nonlinear multi-point boundary value problems.

In this paper, we investigate the existence of positive solutions to nonlinear second-order multi-point boundary value problems:, (1.1), (1.2) where for and , satisfy and . We also make the following assumptions.

() There are real numbers , satisfying on and on , where and or

() there are real numbers , satisfying on and on .