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Differential equations associated with generalized Bell polynomials and their zeros

100%
Ryoo S. C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
807-815
EN
In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.
2
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New interval oscillation criteria for second-order functional differential equations with nonlinear damping

100%
Öǧrekçi S.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
This paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms.We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate our results.
3
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Linear and nonlinear abstract differential equations of high order

88%
Shakhmurov V. B.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established. In application, the separability and spectral properties of nonlocal boundary value problem for the system of degenerate differential equations of infinite order is derived.
4
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Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

75%
Koksal M. E.
Open Mathematics
|
2016
|
tom 14
|
nr 1
693-704
EN
Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.
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