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Existence of three solutions for perturbed nonlinear difference equations

Heidarkhani S., Moghadam M. K.

Opuscula Mathematica

2014

Vol. 34, no. 4

747--761

Using critical point theory, we study the existence of at least three solutions for perturbed nonlinear difference equations with discrete boundary-value condition depending on two positive parameters.

A note on a fourth order discrete boundary value problem

Galewski M., Smejda J.

Opuscula Mathematica

2012

Vol. 32, no. 1

115-123

Using variational methods we investigate the existence of solutions and their dependence on parameters for certain fourth order difference equations.

Positive solutions for discrete boundary value problems with p-Laplacian

Ji D., Ge W.

Journal of Applied Analysis

2010

Vol. 16, nr 1

107-119

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following two-point discrete boundary value problem with p-Laplacian: Δ(∅p(Δu(k - 1))) + e(k)f(u(k)) = 0 , k∈ N(1,T) , u(0) - B0 (Δu(0)) = 0 , u(T + 1) + B1 (Δu(T)) = 0. The main tool is the monotone iterative technique.

A generalized upper and lower solution method for singular discrete boundary value problems for the one-dimensional p-Laplacian

Jiang D. Q., O'Regan D., Agarwal R. P.

Journal of Applied Analysis

2005

Vol. 11, nr 1

35-47

This paper presents new existence results for singular discrete boundary value problems for the one-dimension p-Laplacian. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign. Our results are new even for p = 2