Abstract and Applied Analysis
Volume 2006 (2006), Article ID 54121, 11 pages
doi:10.1155/AAA/2006/54121

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

Abstract

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.