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Classifications and existence of nonoscillatory solutions of second order nonlinear neutral differential equations

Wantong Li (1997)

Annales Polonici Mathematici

A class of neutral nonlinear differential equations is studied. Various classifications of their eventually positive solutions are given. Necessary and/or sufficient conditions are then derived for the existence of these eventually positive solutions. The derivations are based on two fixed point theorems as well as the method of successive approximations.

Commutants of the Dunkl Operators in C(R)

Dimovski, Ivan, Hristov, Valentin, Sifi, Mohamed (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 44A35; 42A75; 47A16, 47L10, 47L80The Dunkl operators.* Supported by the Tunisian Research Foundation under 04/UR/15-02.

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 the third order trinomial differential equations with delay argument

Jozef Džurina, Renáta Kotorová (2009)

Czechoslovak Mathematical Journal

In this paper we study asymptotic properties of the third order trinomial delay differential equation y ' ' ' ( t ) - p ( t ) y ' ( t ) + g ( t ) y ( τ ( t ) ) = 0 by transforming this equation to the binomial canonical equation. The results obtained essentially improve known results in the literature. On the other hand, the set of comparison principles obtained permits to extend immediately asymptotic criteria from ordinary to delay equations.

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