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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.

Comparison theorems for noncanonical third order nonlinear differential equations

88%

Mojsej I., Ohriska J.

Open Mathematics

2007

tom 5

nr 1

154-163

The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.

Ograniczanie wyników

2 Open Mathematics

1 Baculíková B.

1 Džurina J.

1 Mojsej I.

1 Ohriska J.

1 2010

1 2007

Wyniki wyszukiwania

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

Comparison theorems for noncanonical third order nonlinear differential equations