Abstract
A variety of new existence criteria are presented for boundary value problems for second order differential equations. Our results rely on upper lower type inequalities for the appropriate Green’s functions
Authors
Ravi P. Agarwal,
Florida Institute of Technology, USA
Maria Meehan,
University College Dublin, Ireland
Donal O’Regan,
National University of Ireland, Galway, Ireland
Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Bondary value problems; upper and lower inequalities; Green’s functions; Krasnoselskii’s fixed point theorem; existence criteria.
Paper coordinates
R.P. Agarwal, M. Meehan, D. O’Regan, R. Precup, Location of nonnegative solutions for differential equations on finite and semi-infinite intervals, Dynamic Systems and Applications 12 (2003), 323-332.
About this paper
Journal
Dynamic Systems and Applications
Publisher Name
paper on journal website
Print ISSN
1056-2176
Online ISSN
MR 2020470, Zbl pre02061133.
google scholar link
[1] R.P. Agarwal, M. Meehan and D. O’Regan, Positive L^{p} and continuous solutions for Fredholm integral inclusions, to appear in Set Valued Mappings and Applications in Nonlinear analysis (edite by R.P. Agarwal and D. O’Regan), Gordon and Breach Publishers.
[2] R.P. Agarwal, D. O’Regan and P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer, Dordrecht, 1999.
[3] L.H. Erbe and H. Wang, On the existence of positive solutions or ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994), 743-748.
[4] W. Lian, F. Wong and C. Yeh, On the existence of positive solutions of nonlinear second order differential equations, Proc. Amer. Math. Soc., 124 (1996), 1117-1126.
[5] M. Meehan and D. O’Regan, Multiple nonnegative solutions of nonlinear integral equations on compact and semi-infinite intervals, applicable analysis, 74 (2000), 413-427.
[6] D. O’Regan, Theory of Singular Boundary Value problems, World Scientific, Singapore, 1994.
[7] D.O’Regan, Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer, Dordrecht, 1997.
[8] D.O’Regan and R. Precup, Theorems of Leray-Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001.