Oscillation of solutions of some generalized nonlinear α-difference equations - Manuel , Mariasebastin Maria Susai; Kılıçman, Adem; Srinivasan, K.; Babu, G. Dominic (SpringerOpen, 2014)
In this paper, the authors discuss the oscillation of solutions of some generalized nonlinear α-difference equation Δα(ℓ)(p(k)Δα(ℓ)u(k))+q(k)f(u(k−τ(k)))=0,(1) k∈[a,∞), where the functions p, q, f and τ are defined in their domain of definition and α>1, ℓ is a positive real. Further, uf(u)>0 for u≠0, p(k)>0 and limk→∞(k−τ(k))=∞, where Rk=∑[k−ℓℓ]r=01αrp(rℓ)→∞ as k→∞ and u(k) is defined for k≥mini≥0(i−τ(i)) for all k∈[a,∞) for some a∈[0,∞).