On constant-sign solutions of a system of discrete equations

Authors:
Ravi P. Agarwal;Donal O'Regan;Patricia J. Y. Wong
Affiliations:
Department of Mathematical Sciences, Florida Institut of Technology, Melbourne, FL;Department of Mathematics, National University of Ireland, Galway, Ireland;School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
Venue:
Journal of Applied Mathematics and Computing
Year:
1986

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Abstract

We consider the following system of discrete equations ui(k) = ΣNl=0gi(k,l)fi(l, u1(l), u2(l), ..., un(l)), k ∈ {0, 1, ..., T}, 1 ≤ i ≤ n where T ≥ N 0, 1 ≤ i ≤ n. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on {0, 1,...} ui(k) = Σ∞l=0gi(k, l)fi(l, u1(l), u2(l), ..., un(l)), k ∈ {0, 1, ...}, 1 ≤ i ≤ n for which the existence of constant-sign solutions is investigated.