Adjoint operator of the periodic problem for linear differential equations with deviating arguments

1989 ◽  
Vol 44 (5) ◽  
pp. 701-705
Author(s):  
V. G. Nikitin
Keyword(s):  
Differential Equations ◽  
Adjoint Operator ◽  
Periodic Problem ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
Linear Differential

Oscillatory and asymptotic behaviour of all solutions of differential equations with deviating arguments

1978 ◽  
Vol 81 (3-4) ◽  
pp. 195-210 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Unknown Function ◽  
Continuous Functions ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential ◽  
Image Position

SynopsisThis paper deals with the oscillatory and asymptotic behaviour of all solutions of a class of nth order (n > 1) non-linear differential equations with deviating arguments involving the so called nth order r-derivative of the unknown function x defined bywhere r1, (i = 0,1,…, n – 1) are positive continuous functions on [t0, ∞). The results obtained extend and improve previous ones in [7 and 15] even in the usual case where r0 = r1 = … = rn–1 = 1.

Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments

2017 ◽  
Vol 67 (3) ◽  
Author(s):  
Simona Fišnarová ◽  
Robert Mařík
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Linear Differential

AbstractIn this paper we derive oscillation criteria for the second order half-linear neutral differential equationwhere Φ(

scholarly journals Bernstein Widths of Some Classes of Functions Defined by a Self-Adjoint Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Guo Feng
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Differential Operators ◽  
Sobolev Class ◽  
Adjoint Operator ◽  
Linear Differential Equations ◽  
Periodic Functions ◽  
Linear Differential Operators ◽  
Linear Differential ◽  
Special Case

We consider the classes of periodic functions with formal self-adjoint linear differential operatorsWp(ℒr), which include the classical Sobolev class as its special case. Using the iterative method of Buslaev, with the help of the spectrum of linear differential equations, we determine the exact values of Bernstein width of the classesWp(ℒr)in the spaceLqfor1<p≤q<∞.

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