Periodic and subharmonic solutions for a 2nth-order difference equationcontaining both advance and retardation with ϕ-Laplacian

Existence of periodic solutions for a 2nth-order difference equation involving p-Laplacian∗

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...

EXISTENCE OF PERIODIC SOLUTIONS FOR 2nTH-ORDER NONLINEAR p-LAPLACIAN DIFFERENCE EQUATIONS

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...

Existence of Periodic and Subharmonic Solutions for Second-Order p-Laplacian Difference Equations

where Δ is the forward difference operator Δxn = xn+1 − xn, Δxn = Δ(Δxn), φp(s) is p-Laplacian operator φp(s) = |s|p−2s (1 < p < ∞), and f : Z×R3 → R is a continuous functional in the second, the third, and fourth variables and satisfies f (t +m,u,v,w) = f (t,u,v,w) for a given positive integerm. We may think of (1.1) as being a discrete analogue of the second-order functional differential equa...

Multiple periodic solutions for two classes of nonlinear difference systems involving classical ( φ 1 , φ 2 ) - Laplacian

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving (φ1,φ2)-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we establish an existence theorem of three periodic solutions for the first nonlinear difference system with (φ1,φ2)-Laplacian and two parameters. Moreover, for the second no...

Existence of Subharmonic Solutions for a Class of Second-Order p-Laplacian Systems with Impulsive Effects