Original Research

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

  • Alex P. PalamidesAffiliated withDepartment of Electronic Computing Systems, Technological Educational Institute of Piraeus Email author 
  • , Anastasia VeloniAffiliated withDepartment of Electronic Computing Systems, Technological Educational Institute of Piraeus
  • , Stamatis AlatsathianosAffiliated withDepartment of Electronic Computing Systems, Technological Educational Institute of Piraeus

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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