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On the asymptotic behavior of a class of third order nonlinear neutral differential equations

100%

Baculíková B., Džurina J.

Open Mathematics

2010

tom 8

nr 6

1091-1103

The objective of this paper is to study asymptotic properties of the third-order neutral differential equation $$ \left[ {a\left( t \right)\left( {\left[ {x\left( t \right) + p\left( t \right)x\left( {\sigma \left( t \right)} \right)} \right]^{\prime \prime } } \right)^\gamma } \right]^\prime + q\left( t \right)f\left( {x\left[ {\tau \left( t \right)} \right]} \right) = 0, t \geqslant t_0 . \left( E \right) $$. We will establish two kinds of sufficient conditions which ensure that either all nonoscillatory solutions of (E) converge to zero or all solutions of (E) are oscillatory. Some examples are considered to illustrate the main results.

Oscillation of second-order linear delay differential equations

76%

Ohriska J.

Open Mathematics

2008

tom 6

nr 3

439-452

The aim of this paper is to derive sufficient conditions for the linear delay differential equation (r(t)y′(t))′ + p(t)y(τ(t)) = 0 to be oscillatory by using a generalization of the Lagrange mean-value theorem, the Riccati differential inequality and the Sturm comparison theorem.

Ograniczanie wyników

2 Open Mathematics

1 Baculíková B.

1 Džurina J.

1 Ohriska J.

1 2010

1 2008

Wyniki wyszukiwania

On the asymptotic behavior of a class of third order nonlinear neutral differential equations

Oscillation of second-order linear delay differential equations