Existence criteria for a system of two point boundary value problems

Abstract

We consider the following system

where T≥1 and for each 1 ≤ i ≤ n, α_i > 0, γ_i > o, β_i ≥ 0, δ_i ≥ γ_i and α_iγ_i(T+1)+α_iδ_i+β_iγ_i>0. Criteria are offered for the existence of single and double solutions u = u₁u₂,…,u_n) of the system such that each 1 ≤ i ≤ n, we have θ,u_i ≥ 0 on {0,1,…,T+2} where θ_i≥ {1,-1}.

Keywords:

• Fixed sign solutions
• system of difference equations