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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 results for second order nonlinear differential equations

100%

Džurina J., Lacková D.

Open Mathematics

2004

tom 2

nr 1

57-66

In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential equations of the form $$\left( {r\left( t \right)\psi \left( {x\left( t \right)} \right)\left[ {x\left( t \right) + p\left( t \right)x\left( {\tau \left( t \right)} \right)} \right]^\prime } \right)^\prime + q\left( t \right)f\left( {x\left[ {\sigma \left( t \right)} \right]} \right) = 0$$ . Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0.

Ograniczanie wyników

2 Open Mathematics

2 Džurina J.

1 Baculíková B.

1 Lacková D.

1 2010

1 2004

Wyniki wyszukiwania

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

Oscillation results for second order nonlinear differential equations