Sequences of small homoclinic solutions for difference equations on integers
Date
2017-09-22
Authors
Steglinski, Robert
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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].
Description
Keywords
Difference equations, Discrete p-Laplacian, Variational methods, Infinitely many solutions
Citation
Steglinski, R. (2017). Sequences of small homoclinic solutions for difference equations on integers. <i>Electronic Journal of Differential Equations, 2017</i>(228), pp. 1-12.
Rights
Attribution 4.0 International