Positive solutions of functional difference equations with p-Laplacian operator
© Chang-Xiu Song 2006
Received: 18 October 2005
Accepted: 10 January 2006
Published: 31 May 2006
The author studies the boundary value problems with p-Laplacian functional difference equation Δφ p (Δx(t)) + r(t)f(x t ) = 0, t ∈ [0, N], x0 = ψ ∈ C+, x(0) - B0(Δx(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.
- 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
- 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
- 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
- Henderson J: Positive solutions for nonlinear difference equations. Nonlinear Studies 1997,4(1):29–36.MathSciNetMATHGoogle Scholar
- 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
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.