Differential Equations and Dynamical Systems

, Volume 21, Issue 3, pp 261–279

Positive Solutions of a Third-Order BVP Independent of the Sign of the Green’s Function

Authors

    • Department of Electronic Computing SystemsTechnological Educational Institute of Piraeus
  • Anastasia Veloni
    • Department of Electronic Computing SystemsTechnological Educational Institute of Piraeus
  • Stamatis Alatsathianos
    • Department of Electronic Computing SystemsTechnological Educational Institute of Piraeus
Original Research

DOI: 10.1007/s12591-012-0151-5

Cite this article as:
Palamides, A.P., Veloni, A. & Alatsathianos, S. Differ Equ Dyn Syst (2013) 21: 261. doi:10.1007/s12591-012-0151-5

Abstract

A third-order three-point boundary value problem (BVP) is studied, through this work. We derive sufficient conditions that guarantee the positivity of the solution of the corresponding linear boundary value problem (see Proposition 2). Then, based on the classical Guo-Krasnoselskii fixed point theorem, we obtain positive solutions of the nonlinear BVP. The proposed method may be useful, in cases where the Green’s function changes its sign. A BVP that falls in this category is studied through this paper.

Keywords

Three-point singular boundary value problem Third-order differential equation Positive solution Fixed point in cones Green’s functions

Mathematics Subject Classification (1991)

34B10 34B18 34B15 34G20

Copyright information

© Foundation for Scientific Research and Technological Innovation 2012