All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 58 Next

Displaying 1141 – 1160 of 1228

Showing per page

Asymptotic properties of one differential equation with unbounded delay

Zdeněk Svoboda (2012)

Mathematica Bohemica

We study the asymptotic behavior of the solutions of a differential equation with unbounded delay. The results presented are based on the first Lyapunov method, which is often used to construct solutions of ordinary differential equations in the form of power series. This technique cannot be applied to delayed equations and hence we express the solution as an asymptotic expansion. The existence of a solution is proved by the retract method.

Asymptotic properties of solutions of functional differential systems

Anatolij F. Ivanov, Pavol Marušiak (1992)

Mathematica Bohemica

In the paper we study the existence of nonoscillatory solutions of the system x i ( n ) ( t ) = ∑ j = 1 2 p i j ( t ) f i j ( x j ( h i j ( t ) ) ) , n ≥ 2 , i = 1 , 2 , with the property l i m t → ∞ x i ( t ) / t k i = c o n s t ≠ 0 for some k i ∈ { 1 , 2 , ... , n - 1 } , i = 1 , 2 . Sufficient conditions for the oscillation of solutions of the system are also proved.

Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral type

Takaŝi Kusano, Pavol Marušiak (2000)

Mathematica Bohemica

This paper establishes existence of nonoscillatory solutions with specific asymptotic behaviors of second order quasilinear functional differential equations of neutral type. Then sufficient, sufficient and necessary conditions are proved under which every solution of the equation is either oscillatory or tends to zero as t → ∞ .

Asymptotic properties of third order functional dynamic equations on time scales

I. Kubiaczyk, S. H. Saker (2011)

Annales Polonici Mathematici

The purpose of this paper is to study the asymptotic properties of nonoscillatory solutions of the third order nonlinear functional dynamic equation [ p ( t ) [ ( r ( t ) x Δ ( t ) ) Δ ] γ ] Δ + q ( t ) f ( x ( τ ( t ) ) ) = 0 , t ≥ t₀, on a time scale , where γ > 0 is a quotient of odd positive integers, and p, q, r and τ are positive right-dense continuous functions defined on . We classify the nonoscillatory solutions into certain classes C i , i = 0,1,2,3, according to the sign of the Δ-quasi-derivatives and obtain sufficient conditions in order that C i = ∅ . Also, we establish...

Currently displaying 1141 – 1160 of 1228