A Topological Method for Vector-Valued and Nth Order Nonlinear Boundary Value Problems

Abstract

**Please note that the full text is embargoed** ABSTRACT: The use of topological methods in the analysts of second order nonlinear boundary value problems (BVP for short) in Rn of the form (E) [see pdf for notation] (C) [see pdf for notation] has recently attracted the interest of many authors (e.g. [1], [4], [5],[8],[11]) for the case in which n = 1. The prevalent approaches have been the topological method of Wazewski [1,8], the shooting method via the maximum principle, and the Kneser-Hukuhara continuum theorem [1]. A common ingredient in these approaches is the use of upper and lower solutions to obtain bounds on the solutions.