Nonlinear Two-Point Boundary Value Problems with Multiple Solutions

Abstract

In the first part of this paper we study the convergence of finite difference methods to approximate the maximal solution of problems of the forms: u"+ f(x,u) = 0, with boundary conditions either u(0) = u(b) = 0 or U90) = u'(b) - 0, 0<b<1. The function f(x,u) satisfies several conditions that are explicityly give 1. This work extends earler results of Parter (see references atg the end). Since this problem has in general more than one solution we devleop in the second part two algorithms to approximate solutions characterized by the number of their zeros in (0,1). We include in the last section numerical results and some additional comments on the implementation of the algorithms on a digital computer.</dcvalue> <dcvalue element="format" qualifier="mimetype">application/pdf