Bounded Positive Solutions for a Third Order Discrete Equation - Zeqing Liu; Ming Jia; Shin Min Kang; Young Chel Kwun (Abstract and Applied Analysis)
This paper studies the following third order neutral delay discrete equation Δ(anΔ2(xn+pnxn-τ))+f(n,xn-d1n,…,xn-dln)=gn,n≥n0, where τ,l∈ℕ, n0 ∈ℕ∪{0}, ann∈ℕn0, pnn∈ℕn0, gnn∈ℕn0 are real sequences with an≠0 for n≥n0, dinn∈ℕn0⊆ℤ with lim n→∞(n-din)=+∞ for i∈{1,2,…,l} and f∈C(ℕn0×ℝl,ℝ). By using a nonlinear alternative theorem of Leray-Schauder type, we get sufficient conditions which ensure the existence of bounded positive solutions for the equation. Three examples are given to illustrate the results obtained in this paper.