Displaying similar documents to “On the asymptotic classes of solutions of a superlinear differential equation”

Unbounded solutions of third order delayed differential equations with damping term

Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, Mauro Marini (2011)

Open Mathematics

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Globally positive solutions for the third order differential equation with the damping term and delay, x ' ' ' + q ( t ) x ' ( t ) - r ( t ) f ( x ( φ ( t ) ) ) = 0 , are studied in the case where the corresponding second order differential equation y ' ' + q ( t ) y = 0 is oscillatory. Necessary and sufficient conditions for all nonoscillatory solutions of (*) to be unbounded are given. Furthermore, oscillation criteria ensuring that any solution is either oscillatory or unbounded together with its first and second derivatives are presented. The comparison of results...

Comparison theorems for noncanonical third order nonlinear differential equations

Ivan Mojsej, Ján Ohriska (2007)

Open Mathematics

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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.