9 research outputs found
Differenciál- és differenciaegyenletek kvalitatív és kvantitatív elmélete alkalmazásokkal = Qualitative and quantitative theory of differential and difference equations with applications
Kutatásaink a következő témakörökhöz kapcsolódtak: Megoldások aszimptotikus jellemzése és stabilitása; integrálegyenletek és egyenlőtlenségek mértékterekben; differenciálegyenletek megoldásainak paraméterektől való differenciálható függése, paraméterek becslése; állapotfüggő késleltetésű differenciálegyenletek stabilitása. A 2004-2007 kutatási időszakban 31 publikációnk jelent meg. Dolgoztainkra az elmúlt négy évben 575, ezen belül a kutatási periódusban megjelent 31 publikációnkra pedig 57 hivatkozást regisztráltunk. Eredményeinkről 9 plenáris, 33 meghívott szekció és 16 szekció előadásban számoltunk be nemzetközi konferenciákon. Ezeken kívül 34 meghívott előadást tartottunk különböző hazai és külföldi egyetemek szakmai szemináriumain. | Our research is related to the following topics: Asymptotic characterization and stability of solutions; integral equations and inequalities in measure spaces; differentiability of the solutions with respect to the parameters, and parameter estimation methods; stability of differential equations with state-dependent delays. 31 of our pubications have appeared in the research period 2004-2007. We have counted 575 citations of our papers in the last four years, including 57 citations of our 31 papers published in this period. We gave 9 plenary, 33 invited, and 16 contributed talks at international conferences, and 34 invited talks at research seminars of national and foreign universities
Existence of -bounded solutions for nonhomogeneous Lyapunov matrix differential equations on
In this paper, we give a necessary and sufficient condition for the existence of at least one -bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation on . In addition, we give a result in connection with the asymptotic behavior of the -bounded solution of this equation
Bohl-Perron type stability theorems for linear difference equations with infinite delay
Relation between two properties of linear difference equations with infinite
delay is investigated: (i) exponential stability, (ii) \l^p-input
\l^q-state stability (sometimes is called Perron's property). The latter
means that solutions of the non-homogeneous equation with zero initial data
belong to \l^q when non-homogeneous terms are in \l^p. It is assumed that
at each moment the prehistory (the sequence of preceding states) belongs to
some weighted \l^r-space with an exponentially fading weight (the phase
space). Our main result states that (i) (ii) whenever and a certain boundedness condition on coefficients is
fulfilled. This condition is sharp and ensures that, to some extent,
exponential and \l^p-input \l^q-state stabilities does not depend on the
choice of a phase space and parameters and , respectively. \l^1-input
\l^\infty-state stability corresponds to uniform stability. We provide some
evidence that similar criteria should not be expected for non-fading memory
spaces.Comment: To be published in Journal of Difference Equations and Application
Existence of Ψ−bounded solutions for nonhomogeneous Lyapunov matrix differential equations on R
In this paper, we give a necessary and sufficient condition for the existence of at least one -bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation on . In addition, we give a result in connection with the asymptotic behavior of the -bounded solution of this equation
Perron-Type Criterion for Linear Difference Equations with Distributed Delay
It is shown that if a linear difference equation with distributed delay of the form Δx(n) , n ≥ 1, satisfies a Perron condition then its trivial solution is uniformly asymptotically stable
A criterion for the exponential stability of linear difference equations
AbstractWe give an affirmative answer to a question formulated by Aulbach and Van Minh by showing that the linear difference equation xn+1=Anxn,forn∈N in a Banach space B is exponentially stable if and only if for every f = {fn}n=1∞ ∈ lp(NB), where I < p < ∞, the solution of the Cauchy problem xn+1=Anxn+fn,forn∈N,x1=0 is bounded on N