INFORMATION CHANGE THE WORLD

International Journal of Engineering and Manufacturing(IJEM)

ISSN: 2305-3631 (Print), ISSN: 2306-5982 (Online)

Published By: MECS Press

IJEM Vol.2, No.1, Feb. 2012

Multiple Positive Solutions of Two-Point Boundary Value Problems for Systems of Nonlinear Third-Order Differential Equations

Full Text (PDF, 265KB), PP.78-87


Views:66   Downloads:1

Author(s)

Zhongmin Sun,Suoquan Ren,Zhenlin Wu,Huabin Zhang

Index Terms

Boundary value problems; Positive solutions; Green's functions; cones

Abstract

In this paper, we study the two-point boundary value problems for systems of nonlinear third-order dierential equations .Under some conditions, we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point theorems in cones.

Cite This Paper

Zhongmin Sun,Suoquan Ren,Zhenlin Wu,Huabin Zhang,"Multiple Positive Solutions of Two-Point Boundary Value Problems for Systems of Nonlinear Third-Order Differential Equations", IJEM, vol.2, no.1, pp.78-87, 2012.

Reference

[1]D. R. Anderson, Green's function for a third-order generalized right focal problem, J. Math. Anal. Appl.288 (2003) 1-14.

[2]D. R. Anderson, J. M. Davis, Multiple solutions and eigenvalues for three-order right focal boundary value problems, J. Math. Anal. Appl.267(2002) 135-157.

[3]R. Ma, Multiplicity results for a third order boundary value problem at resonance, Nonliner Anal. TMA 32(4)(1998)493-499

[4]Y. Sun, Positive solutions of a singular third-order three-point boundary value problem, J. Math. Appl.306(2005)589-603.

[5]Q. Yao. The existence and multiplicity of positive solutions for a third-order three-point boundary value problem, Acta Math. Appl 2003, 19: 117-122.

[6]M. E. Shahed, Positive solutions for nonlinear singular third order boundary value problem, Communications in Nonlinear Science and Numerical Simulation. 14(2009): 424-429.

[7]Z. L. Yang, J. X. Sun, Positive solutions of boundary value problems for system of nonlinear second order ordinary dierential equations, Acta Math.Sinica, 47(1)(2004):111-118.

[8]R. P. Agarwal, D. O'Regan, P. J. Y. Wong. Positive Solutions of Dierential,Dierence and Integral Equations, Kluwer, Dordrecht, 1999.

[9]Klaus Deiming, Nonlinear Functional Analysis,Springer-Verlag, New York, 1985

[10]Dajun Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Boston,1988

[11]M. A. Krasbosel'skii. Positive Solutions of Operator Equations, Noordho, Groningen, 1964.