Displaying similar documents to “Behaviour of solutions of linear differential equations with delay”

On the oscillation of certain class of third-order nonlinear delay differential equations

S. H. Saker, J. Džurina (2010)

Mathematica Bohemica

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In this paper we consider the third-order nonlinear delay differential equation (*) ( a ( t ) x ' ' ( t ) γ ) ' + q ( t ) x γ ( τ ( t ) ) = 0 , t ≥ t 0 , where a ( t ) , q ( t ) are positive functions, γ > 0 is a quotient of odd positive integers and the delay function τ ( t ) ≤ t satisfies lim t → i n f t y τ ( t ) = i n f t y . We establish some sufficient conditions which ensure that (*) is oscillatory or the solutions converge to zero. Our results in the nondelay case extend and improve some known results and in the delay case the results can be applied to new classes of equations which are not covered by the...

Comparison theorems for the third order trinomial differential equations with delay argument

Jozef Džurina, Renáta Kotorová (2009)

Czechoslovak Mathematical Journal

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In this paper we study asymptotic properties of the third order trinomial delay differential equation y ' ' ' ( t ) - p ( t ) y ' ( t ) + g ( t ) y ( τ ( t ) ) = 0 by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.