On the Kneser-type solutions for two-dimensional linear differential systems with deviating arguments

For the differential system u1 (t)=p(t)u2 ( τ(t)), u2 (t)=q(t)u1 ( σ(t)), t∈[ 0,+∞), where p,q∈L loc ( + ;+), τ,σ∈C( + ;+), lim t→+∞ τ(t)= lim t→+∞ σ(t)=+∞, we get necessary and sufficient conditions that this system does not have solutions satisfying the condition u1 (t)u2 (t)<0 for t∈[ t0,+∞). Note one of our results obtained for this system with constant coefficients and delays ( p(t)≡p,q(t)≡q,τ(t)=t-,σ(t)=t- δ, where δ,∈ and +δ>0). The inequality ( δ+) pq >2/e is necessary and sufficient for nonexistence of solutions satisfying this condition.