Abstract and Applied Analysis
Volume 2006 (2006), Article ID 54121, 11 pages

A symmetric solution of a multipoint boundary value problem at resonance

Nickolai Kosmatov

Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock 72204-1099, AR, USA

Received 18 January 2005; Accepted 1 June 2005

Copyright © 2006 Nickolai Kosmatov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problem u(t)=f(t,u(t),|u(t)|),t(0,1), u(0)=i=1nμiu(ξi),u(1t)=u(t),t[0,1], where 0<ξ1<ξ2<<ξn1/2, i=1nμi=1, f:[0,1]×2 with f(t,x,y)=f(1t,x,y), (t,x,y)[0,1]×2, satisfying the Carathéodory conditions.