By using the critical point theory, the existence of periodic solutions for a 2nth-order nonlinear difference equation containing both advance and retardation involving p-Laplacian is obtained. The main approaches used in our paper are variational techniques and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions for a 2nth-order p-Laplacian difference equation...

By using the critical point theory, the existence of periodic solutions for 2nth-order nonlinear pLaplacian difference equations is obtained. The main approaches used in our paper are variational techniques and the Saddle Point theorem. The problem is to solve the existence of periodic solutions for 2nth-order p-Laplacian difference equations. The results obtained successfully generalize and co...

This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.

this paper is concerned with a 2nth-order p-laplacian difference equation. by using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for neumann boundary value problem and give some new results. results obtained successfully generalize and complement the existing ones.

and Applied Analysis 3 F2 F t, xn, . . . , x0 W t, x0 − H t, xn, . . . , x0 , for every t ∈ Z, W,H are continuously differentiable in x0 and xn, . . . , x0, respectively. Moreover, there is a bounded set J ⊂ Z such that H t, xn, . . . , x0 ≥ 0; 2.2 F3 There is a constant μ > p such that 0 < μW t, x0 ≤ W ′ 2 t, x0 x0, ∀ t, x0 ∈ Z × R \ {0} ; 2.3 F4 H t, 0, . . . , 0 ≡ 0, and there is a constant ...