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  • Research Article
  • Open Access

Positive solutions of functional difference equations with p-Laplacian operator

Advances in Difference Equations20062006:082784

https://doi.org/10.1155/ADE/2006/82784

  • Received: 18 October 2005
  • Accepted: 10 January 2006
  • Published:

Abstract

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 = ψ C+, 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.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation

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Authors’ Affiliations

(1)
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China
(2)
School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510006, China

References

  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.MathSciNetView ArticleMATHGoogle Scholar
  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.MathSciNetView ArticleMATHGoogle Scholar
  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.MathSciNetView ArticleMATHGoogle Scholar
  4. Henderson J: Positive solutions for nonlinear difference equations. Nonlinear Studies 1997,4(1):29–36.MathSciNetMATHGoogle Scholar
  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)00018-0MathSciNetView ArticleMATHGoogle Scholar

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