id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-540	Heidarkhani, Shapour; Gharehgazlouei, Fariba; Imbesi, Maurizio	Existence and multiplicity of homoclinic solutions for a difference equation	2020	12	.pdf	application/pdf	4836	273	75	= 1 p ‖u‖p − ∑ k∈Z H(u(k)) ∀u ∈ X, (2.2) Ψ(u) := ∑ k∈Z F (k, u(k)) ∀ u ∈ lp (2.3) where F (k, t) = ∫ t 0 f(k, ξ)dξ for t ∈ R and k ∈ Z, H(t) = ∫ t 0 h(ξ)dξ for t ∈ R. Let Iλ : X → R be the energy functional associated to the problem (1.1) defined by Iλ(u) = λf(k, u(k)) + sin4( u(k) 2 ) ∀k ∈ Z, u(k)→ 0 as |k| → ∞. For all (k, t) ∈ Z× R put f(k, t)	cache/ejde-540.pdf	txt/ejde-540.txt