Homoclinic solutions of 2nth-order difference equations containing both advance and retardation

Infinitely Many Homoclinic Orbits for 2nth-Order Nonlinear Functional Difference Equations Involving the p-Laplacian

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 ...

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...

Homoclinic Solutions for a Class of Nonlinear Difference Equations

Homoclinic Orbits of Second-order Nonlinear Difference Equations

We establish existence criteria for homoclinic orbits of secondorder nonlinear difference equations by using the critical point theory in combination with periodic approximations.

EXISTENCE OF HOMOCLINIC SOLUTIONS FOR SECOND ORDER DIFFERENCE EQUATIONS WITH p-LAPLACIAN

Using the variational method and critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation −∆ ( a(k)φp(∆u(k − 1)) ) + b(k)φp(u(k)) = λf(k, u(k))), k ∈ Z, where p > 1 is a real number, φp(t) = |t|p−2t for t ∈ R, λ > 0 is a parameter, a, b : Z→ (0,∞), and f : Z × R → R is continuous in the second variable. Related results in the lite...