On the Kneser-Type Solutions for Two-Dimensional Linear Differential Systems with Deviating Arguments

Abstract

For the differential system u1'(t)=p(t)u2(τ(t)), u2'(t)=q(t)u1(σ(t)), t∈[0,+∞), where p,q∈Lloc(ℝ+;ℝ+), τ,σ∈C(ℝ+;ℝ+), limt→+∞τ(t)=limt→+∞σ(t)=+∞, we get necessary and sufficient conditions that this system does not have solutions satisfying the condition u1(t)u2(t)0). The inequality (δ+Δ)pq>2/e is necessary and sufficient for nonexistence of solutions satisfying this condition.