Journal of Inequalities and Applications
Volume 2005 (2005), Issue 4, Pages 363-385

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

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.


We consider the following system of differential equations ui(m)(t)=Pi(t,u1(t),u2(t),,un(t)), t[0,1], 1in together with Hermite boundary conditions ui(j)(tk)=0, j=0,,mk1, k=1,,r, 1in, where 0=t1<t2<<tr=1, mk1 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].