Asymptotic Representations for Solutions of One Class of Systems of Quasilinear Differential Equations

We establish asymptotic representations for solutions of one class of systems of differential equations appearing in the investigation of the asymptotic behavior of nth-order quasilinear differential equations.     

Asymptotic representations of solutions of second-order differential equations

We establish asymptotic representations as t → ω (ω ≤ + ∞) of a class of monotone solutions of the second-order differential equation y″ = f(t, y, y′), where f:[a,ω[× Δ _Y0 × Δ _Y1 is a continuous function asymptotically close on the considered class of solutions to a function of the form ±p(t)φ ₀(y)φ ₁(y′) with functions φ ₀ and φ ₁ regularly varying as y → Y ₀ and y′ → Y ₁. Here Δ _Yi , i ∈ {0, 1}, is a one-sided neighborhood of Y _i , and Y _i is either zero or ±∞.