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Comparison theorems for differential equations of neutral type

Miroslava Růžičková (1997)

Mathematica Bohemica

We are interested in comparing the oscillatory and asymptotic properties of the equations L n [ x ( t ) - P ( t ) x ( g ( t ) ) ] + δ f ( t , x ( h ( t ) ) ) = 0 with those of the equations M n [ x ( t ) - P ( t ) x ( g ( t ) ) ] + δ Q ( t ) q ( x ( r ( t ) ) ) = 0 .

Comparison theorems for functional differential equations

Jozef Džurina (1994)

Mathematica Bohemica

In this paper the oscillatory and asymptotic properties of the solutions of the functional differential equation L n u ( t ) + p ( t ) f ( u [ g ( t ) ] ) = 0 are compared with those of the functional differential equation α n u ( t ) + q ( t ) h ( u [ w ( t ) ] ) = 0 .

Comparison theorems for noncanonical third order nonlinear differential equations

Ivan Mojsej, Ján Ohriska (2007)

Open Mathematics

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.

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