Journal of Inequalities and Applications
Volume 2005 (2005), Issue 4, Pages 363-385
doi:10.1155/JIA.2005.363
Triple fixed-sign solutions in modelling a system with Hermite boundary conditions
School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
Received 21 August 2003; Revised 2 January 2004
Copyright © 2005 Patricia J. Y. Wong and Y. C. Soh. 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.
Abstract
We consider the following system of differential equations
ui(m)(t)=Pi(t,u1(t),u2(t),…,un(t)), t∈[0,1], 1≤i≤n together with Hermite boundary
conditions ui(j)(tk)=0, j=0,…,mk−1, k=1,…,r, 1≤i≤n, where 0=t1<t2<⋯<tr=1, mk≥1 for k=1,…,r, and ∑k=1rmk=m. By using different fixed point theorems, we offer criteria for the
existence of three solutions of the system which are of
“prescribed signs” on the interval [0,1].