Journal of Inequalities and Applications
Volume 6 (2001), Issue 6, Pages 599-624
On the existence of positive solutions for nonlinear two-point boundary-value problems
1Universität Regensburg, Naturwissenschaftliche Fakultät l-Mathematik, Univesitätsstraße 31, Regensburg D-93053, Germany
2lnstitute for Information Transmission Problems, Russian Academy of Sciences, Bol. Karetny lane 19, Moscow 101447, Russia
Received 23 November 1999; Revised 26 January 2000
Copyright © 2001 R. Mennicken and D. Rachinskii. 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.
The paper suggests sufficient conditions for the existence of positive solutions to vector boundary-value problems for second-order differential equations. For potential problems we develop the approach which combines the classical variational method with methods of positive operators. The results are then applied to nonpotential problems where the nonlinearities have potential minorants and majorants.