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

Patricia J. Y. Wong and Y. C. Soh

 School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
Received 21 August 2003; Revised 2 January 2004

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].