Steglinski, Robert2022-07-272022-07-272017-09-22Steglinski, R. (2017). Sequences of small homoclinic solutions for difference equations on integers. <i>Electronic Journal of Differential Equations, 2017</i>(228), pp. 1-12.1072-6691https://hdl.handle.net/10877/15997In this article, we determine a concrete interval of positive parameters λ, for which we prove the existence of infinitely many homoclinic solutions for a discrete problem -Δ(α(k)φp (Δu(k - 1))) + b(k)φp(u(k)) = λƒ(k, u(k)), k ∈ ℤ, where the nonlinear term ƒ : ℤ x ℝ → ℝ has an appropriate oscillatory behavior at zero. We use both the general variational principle of Ricceri and the direct method introduced by Faraci and Kristály [11].Text12 pages1 file (.pdf)enAttribution 4.0 InternationalDifference equationsDiscrete p-LaplacianVariational methodsInfinitely many solutionsArticle