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On L w 2 -quasi-derivatives for solutions of perturbed general quasi-differential equations

Sobhy El-sayed Ibrahim (1999)

Czechoslovak Mathematical Journal

This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of n th order with complex coefficients M [ y ] - λ w y = w f ( t , y [ 0 ] , ... , y [ n - 1 ] ) , t [ a , b ) provided that all r th quasi-derivatives of solutions of M [ y ] - λ w y = 0 and all solutions of its normal adjoint M + [ z ] - λ ¯ w z = 0 are in L w 2 ( a , b ) and under suitable conditions on the function f .

On non-oscillation on semi-axis of solutions of second order deviating differential equations

Sergey Labovskiy, Manuel Alves (2018)

Mathematica Bohemica

We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations u ' ' ( x ) + i p i ( x ) u ' ( h i ( x ) ) + i q i ( x ) u ( g i ( x ) ) = 0 without the delay conditions h i ( x ) , g i ( x ) x , i = 1 , 2 , ... , and u ' ' ( x ) + 0 u ' ( s ) d s r 1 ( x , s ) + 0 u ( s ) d s r 0 ( x , s ) = 0 .

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