Advances in Difference Equations

, 2006:082784 | Cite as

Positive solutions of functional difference equations with p-Laplacian operator

  • Chang-Xiu Song
Open Access
Research Article


The author studies the boundary value problems with p-Laplacian functional difference equation Δφ p x(t)) + r(t)f(x t ) = 0, t ∈ [0, N], x0 = ψC+, x(0) - B0x(0)) = 0, Δx(N+1) = 0. By using a fixed point theorem in cones, sufficient conditions are established for the existence of twin positive solutions.


Differential Equation Partial Differential Equation Ordinary Differential Equation Functional Analysis Functional Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Agarwal RP, Henderson J: Positive solutions and nonlinear eigenvalue problems for third-order difference equations. Computers & Mathematics with Applications 1998,36(10–12):347–355.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Avery RI, Chyan CJ, Henderson J: Twin solutions of boundary value problems for ordinary differential equations and finite difference equations. Computers & Mathematics with Applications 2001,42(3–5):695–704.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Cabada A: Extremal solutions for the difference φ -Laplacian problem with nonlinear functional boundary conditions. Computers & Mathematics with Applications 2001,42(3–5):593–601.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Henderson J: Positive solutions for nonlinear difference equations. Nonlinear Studies 1997,4(1):29–36.MathSciNetMATHGoogle Scholar
  5. 5.
    Liu Y, Ge W: Twin positive solutions of boundary value problems for finite difference equations with p -Laplacian operator. Journal of Mathematical Analysis and Applications 2003,278(2):551–561. 10.1016/S0022-247X(03)00018-0MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Chang-Xiu Song 2006

This article is published under license to BioMed Central Ltd. 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.

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouChina
  2. 2.School of Applied MathematicsGuangdong University of TechnologyGuangzhouChina

Personalised recommendations