Open Access

Triple fixed-sign solutions in modelling a system with Hermite boundary conditions

Journal of Inequalities and Applications20052005:746740

DOI: 10.1155/JIA.2005.363

Received: 21 August 2003

Published: 31 August 2005

Abstract

We consider the following system of differential equations https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq1_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq2_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq3_HTML.gif together with Hermite boundary conditions https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq5_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq6_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq7_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq8_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq9_HTML.gif for https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq10_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq11_HTML.gif . 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 https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.363/MediaObjects/13660_2003_Article_1548_IEq12_HTML.gif .

Authors’ Affiliations

(1)
School of Electrical and Electronic Engineering, Nanyang Technological University

Copyright

© Wong and Soh. 2005