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Nonoscillation Criteria for Two-Dimensional Time-Scale Systems

100%
Öztürk Ö., Akın E.
Nonautonomous Dynamical Systems
|
2016
|
tom 3
|
nr 1
1-13
EN
We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.
2
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On oscillation and nonoscillation properties of Emden-Fowler difference equations

100%
Cecchi M., Došlá Z., Marini M.
Open Mathematics
|
2009
|
tom 7
|
nr 2
322-334
EN
A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation $$ \Delta (a_n \left| {\Delta x_n } \right|^\alpha sgn\Delta x_n ) + b_n \left| {x_{n + 1} } \right|^\beta sgnx_{n + 1} = 0 $$ is given, jointly with some asymptotic properties. The problem of the coexistence of all possible types of nonoscillatory solutions is also considered and a comparison with recent analogous results, stated in the half-linear case, is made.
3
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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
EN
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.
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