Bounded Positive Solutions for a Third Order Discrete Equation

Zeqing Liu, Ming Jia, Shin Min Kang and Young Chel Kwun

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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}, {an} n∈ℕn0, {pn} n∈ℕn0, {gn} n∈ℕn0 are real sequences with an ≠ 0 for n ≥ n0, {din} n∈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.

Date: 2012
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https://doi.org/10.1155/2012/237036

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:237036

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