Asymptotic behaviour of a class of nonoscillatory solutions of differential equations with deviating arguments
Christos G. Philos (1983)
Mathematica Slovaca
N. Parhi, Seshadev Padhi (2000)
Mathematica Slovaca
Josef Kalas, Josef Rebenda (2011)
Mathematica Bohemica
We present several results dealing with the asymptotic behaviour of a real two-dimensional system with bounded nonconstant delays satisfying , under the assumption of instability. Here , and are supposed to be matrix functions and a vector function, respectively. The conditions for the instable properties of solutions together with the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the real system considered to one equation with...
Božena Mihalíková (1990)
Mathematica Slovaca
Josef Kalas (1981)
Archivum Mathematicum
Monika Sobalová (2002)
Archivum Mathematicum
In the paper the fourth order nonlinear differential equation , where , , , and for is considered. We investigate the asymptotic behaviour of nonoscillatory solutions and give sufficient conditions under which all nonoscillatory solutions either are unbounded or tend to zero for .
Miroslav Bartušek, Jan Osička (2002)
Mathematica Bohemica
Asymptotic behaviour of oscillatory solutions of the fourth-order nonlinear differential equation with quasiderivates is studied.
Miroslav Bartušek (1997)
Czechoslovak Mathematical Journal
Sufficient conditions are given under which the sequence of the absolute values of all local extremes of , of solutions of a differential equation with quasiderivatives is increasing and tends to . The existence of proper, oscillatory and unbounded solutions is proved.
Georgiev, Svetlin (2000)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
Werner Kratz (1988)
Czechoslovak Mathematical Journal
Jozef Rovder (1986)
Archivum Mathematicum
N. Parhi, Seshadev Padhi (2001)
Archivum Mathematicum
This paper deals with property A and B of a class of canonical linear homogeneous delay differential equations of -th order.
Josef Diblík (1993)
Annales Polonici Mathematici
Inequalities for some positive solutions of the linear differential equation with delay ẋ(t) = -c(t)x(t-τ) are obtained. A connection with an auxiliary functional nondifferential equation is used.
Evtukhov, V.M., Shebanina, E.V. (1998)
Memoirs on Differential Equations and Mathematical Physics
Josef Rebenda (2009)
Archivum Mathematicum
In this article, stability and asymptotic properties of solutions of a real two-dimensional system are studied, where , are matrix functions, is a vector function and is a nonconstant delay which is absolutely continuous and satisfies . Generalization of results on stability of a two-dimensional differential system with one constant delay is obtained using the methods of complexification and Lyapunov-Krasovskii functional and some new corollaries and examples are presented.
Jan Čermák (2000)
Mathematica Bohemica
In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y’(x)=a(x)y((x))+b(x)y(x), xI=[x0,). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z’(x)=b(x)z(x), xI and a solution of the functional equation |a(x)|((x))=|b(x)|(x), xI.
Jozef Miklo (1988)
Mathematica Slovaca
Jozef Rovder (1980)
Mathematica Slovaca
Anna Andruch-Sobiło, Andrzej Drozdowicz (2008)
Mathematica Bohemica
In the paper we consider the difference equation of neutral type where ; , is strictly increasing and is nondecreasing and , , . We examine the following two cases: and where , are positive integers. We obtain sufficient conditions under which all nonoscillatory solutions of the above equation tend to zero as with a weaker assumption on than the...
Roman Koplatadze, N. L. Partsvania, Ioannis P. Stavroulakis (2003)
Archivum Mathematicum
Sufficient conditions are established for the oscillation of proper solutions of the system where are locally summable functions, while and are continuous and continuously differentiable functions, respectively, and , .