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Comparison theorems for noncanonical third order nonlinear differential equations

100%
Mojsej I., Ohriska J.
Open Mathematics
|
2007
|
tom 5
|
nr 1
154-163
EN
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.
2
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On solutions of third order nonlinear differential equations

100%
Mojsej I., Ohriska J.
Open Mathematics
|
2006
|
tom 4
|
nr 1
46-63
EN
The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.
3
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On bounded nonoscillatory solutions of third-order nonlinear differential equations

100%
Mojsej I., Tartaľová A.
Open Mathematics
|
2009
|
tom 7
|
nr 4
717-724
EN
This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. We give the necessary and sufficient conditions guaranteeing the existence of bounded nonoscillatory solutions. Sufficient conditions are proved via a topological approach based on the Banach fixed point theorem.
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