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 literature are extended.