ON PERIODIC BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR FUNCTIONAL DIFFERENCE EQUATIONS WITH p-LAPLACIAN

Motivated by (Linear Algebra and its Appl. 420 (2007), 218- 227) and (Linear Algebra and its Appl. 425 (2007), 171-183), we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional dierence equations with p-Laplacian. Su- cient conditions for the existence of at least one solution of this problem are established.

[1]  V. Kocić,et al.  Global Behavior of Nonlinear Difference Equations of Higher Order with Applications , 1993 .

[2]  Alberto Cabada,et al.  Existence and uniqueness results for discrete second-order periodic boundary value problems , 2003 .

[3]  Yi Wang,et al.  Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions ✩ , 2005 .

[4]  K. Deimling.  Nonlinear functional analysis , 1985 .

[5]  Alberto Cabada,et al.  Extremal solutions for the difference φ-Laplacian problem with nonlinear functional boundary conditions☆ , 2001 .

[6]  R. Mickens.  Periodic Solutions of Second-order Nonlinear Difference Equations Containing a Small Parameter—III. Perturbation Theory , 1986 .

[7]  Periodic solutions of second-order nonlinear difference equations containing a small parameter. IV: Multi-discrete time method , 1987 .

[8]  Ravi P. Agarwal,et al.  Focal Boundary Value Problems for Differential and Difference Equations , 1998 .

[9]  D. O’Regan,et al.  Positive Solutions of Differential, Difference and Integral Equations , 1998 .

[10]  G. Guseinov,et al.  Positive Periodic Solutions for Nonlinear Difference Equations with Periodic Coefficients , 1999 .

[11]  A. Cabada,et al.  Existence and Comparison Results for Difference φ-Laplacian Boundary Value Problems with Lower and Upper Solutions in Reverse Order , 2002 .

[12]  J. Ji,et al.  Eigenvalue comparisons for boundary value problems for second order difference equations , 2006 .