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A note on comparison theorems for third-order linear differential equations
... The problems of existence of monotone or Kneser solutions for third order ordinary differential equations with quasi-derivatives were studied in several papers ( [5], [7], [8], [10]). The equation (L), where p{(t) = 1, i = 1,2,3 (n = 4) was studied, for example, in ( [6], [9], [12]). ...
The paper deals with the existence of Kneser solutions to nth-order nonlinear differential equations with quasiderivatives.
The paper presents two different approaches to estimating the region of stability of differential equation. Estimation of the region of stability is an essential practice in relation to control of the dynamical system. In this paper the objects of examination are differential equations with quasi-derivation. The equations have features that do not allow the application of classical methods for establishing stability. The goal is to compare the results of an analytic approach using Lyapunov method and computer simulation using a numerical method. The brief description of both methods are introduced and graphical results are presented and compared
The existence and uniqueness of monotone solution of linear differential equation of the third order are proved. Using Ky Fan fixed-point theorem the existence of such solution of nonlinear equation of the third order is obtained.
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