Yazar "Demidenko, Gennadii" seçeneğine göre listele

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  • Küçük Resim
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    On asymptotic stability of solutions to nonlinear systems of differential equations with periodic coefficients
    (Selcuk University Research Center of Applied Mathematics, 2002) Demidenko, Gennadii; Matveeva, Inessa
    This paper is devoted to the study of a nonlinear system of differential equations with two parameters. We determine values of the parameters under which solutions to the system are asymptotically stable. We obtain also estimates enabling us to indicate the decay rate of solutions at infinity.
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    On location of the matrix spectrum inside an elipse
    (Selcuk University Research Center of Applied Mathematics, 2003) Bulgak, Ayşe; Demidenko, Gennadii; Matveeva, Inessa
    In the present article we consider the problem on location of the spectrum of an arbitrary matrix $A$ inside the ellipse calE=lambdainC:frac(Relambda)2a2+frac(Imlambda)2b2=1,quada>b. calE=lambdainC:frac(Relambda)2a2+frac(Imlambda)2b2=1,quada>b. One of the authors (see~[9]) established a connection of the problem with solvability of the matrix equation H?left(frac12a2+frac12b2ight)A?HA?left(frac14a2?frac14b2ight)(HA2+(A?)2H)=C. H?left(frac12a2+frac12b2ight)A?HA?left(frac14a2?frac14b2ight)(HA2+(A?)2H)=C. In this article we construct a Hermitian positive definite solution $H$ to the equation in the form of a power series. We prove that the norm $|H|$ characterizes an immersion depth of eigenvalues of the matrix $A$ in the inside of the ellipse ${cal E}$. On the base of these results we propose an algorithm to determine whether the spectrum of the matrix $A$ belongs to the inside of the ellipse ${cal E}$.
  • Küçük Resim
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    On properties of a class of matrix differential operators in R?
    (Selcuk University Research Center of Applied Mathematics, 2002) Demidenko, Gennadii
    In the paper we consider a class of matrix quasi-elliptic operators in $R^n$. We establish isomorphic properties of these operators in special weighted Sobolev spaces $W^l_{p,sigma}(R^n)$. From our results a theorem on isomorphism for the Navier-Stokes operator follows.