The iterative solutions of 2 nth-order nonlinear multi-point boundary value problems

Abstract

The aim of this paper is to investigate the existence of iterative solutions for a class of 2 nth-order nonlinear multi-point boundary value problems. The multi-point boundary condition under consideration includes various commonly discussed boundary conditions, such as three- or four-point boundary condition, ( n + 2)-point boundary condition and 2( n − m)-point boundary condition. The existence problem is based on the method of upper and lower solutions and its associated monotone iterative technique. A monotone iteration is developed so that the iterative sequence converges monotonically to a maximal solution or a minimal solution, depending on whether the initial iteration is an upper solution or a lower solution. Two examples are presented to illustrate the results.