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Oscillation theorems for neutral differential equations with the quasi-derivatives

Miroslava Růžičková, E. Špániková (1994)

Archivum Mathematicum

The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives L n [ x ( t ) + ( - 1 ) r P ( t ) x ( g ( t ) ) ] + δ Q ( t ) f ( x ( h ( t ) ) ) = 0 , where n 2 , r { 1 , 2 } , and δ = ± 1 . There are given sufficient conditions for solutions to be either oscillatory or they converge to zero.

Oscillatory and asymptotic behaviour of solutions of advanced functional equations

Jozef Džurina (1993)

Archivum Mathematicum

In this paper we compare the asymptotic behaviour of the advanced functional equation L n u ( t ) - F ( t , u [ g ( t ) ] ) = 0 with the asymptotic behaviour of the set of ordinary functional equations α i u ( t ) - F ( t , u ( t ) ) = 0 . On the basis of this comparison principle the sufficient conditions for property (B) of equation (*) are deduced.

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