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1.
Sufficient conditions are established for the existence of almost periodic solutions for strongly stable nonlinear impulsive differential-difference equations. The investigations are carried out by means of piecewise continuous functions of Lyapunov type and by using Markoff’s sets. We provide an example to demonstrate the effectiveness of our results. 相似文献
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On almost periodic processes in impulsive competitive systems with delay and impulsive perturbations
In the present paper we investigate the existence of almost periodic processes of ecological systems which are presented with the general impulsive nonautonomous Lotka–Volterra system of integro-differential equations with infinite delay. The impulses are at fixed moments of time, and by using the techniques of piecewise continuous Lyapunov’s functions, new sufficient conditions for the global exponential stability of the unique positive almost periodic solutions of these systems are given. 相似文献
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Existence of almost periodic solutions for strong stable impulsive differential equations 总被引:1,自引:0,他引:1
Conditions for strong stability and the existence of almostperiodic solutions of systems of impulsive differential equationswith impulsive effect at fixed moments are obtained. The investigationsare carried out by means of piecewise continuous functions whichare analogues of Lyapunov functions. 相似文献
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Manuel Pinto 《Applied mathematics and computation》2010,217(8):4167-4177
The existence and global exponential stability of an almost periodic solution of an impulsive neural network model with distributed delays is considered in a matrix setting. The approach transforms the original network into a matrix analysis problem, where a set of sufficient conditions based on spectral radius is presented. A concrete Hopfield model shows the advantages in comparison with a classical norm approach. 相似文献
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Summary In a recent paper [J. Diff. Equat. 55 (2) (1984), 225–256], J. Palmer proved Smale's theorem on the embedding of the Bernoulli shift in the context of a periodic differential system (*)
=f (t, x),x
n
, using a nonautonomous shadow lemma. By means of this lemma, we show that one does get a similar kind of chaotic motion whenf is almost periodic int. Actually, we do not consider the equation (*). In order to show that the hypotheses can be satisfied, we rather consider a parameter-dependent equation of the formx=g(x)+h(t,x,), whereIR is the parameter.
Zusammenfassung In einer kürzlich erschienenen Arbeit [J. Diff. Equat. 55 (2) (1984), 225–256] bewies J. Palmer den Satz von Smale über die Einbettung des Bernoullischifts für periodische Differentialgleichungssysteme der Form (*) =f (t, x),x n , unter Verwendung eines Schattenlemmas für nicht-autonome Systeme. Mit Hilfe dieses Lemmas zeigen wir, daß man eine ähnliche chaotische Bewegung erhält, wennf fast-periodisch int ist. Genau genommen betrachten wir nicht die Gleichung (*). Um zu zeigen, daß die Voraussetzungen erfüllt werden können, betrachten wir vielmehr eine parameterabhängige Gleichung der Form =g(x)+h(t,x,), wobeiIR der Parameter ist.相似文献
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Michal Veselý 《Journal of Difference Equations and Applications》2013,19(10):1623-1647
Almost periodic homogeneous linear difference systems are considered. It is supposed that the coefficient matrices belong to a group. The aim was to find such groups that the systems having no non-trivial almost periodic solution form a dense subset of the set of all considered systems. A closer examination of the used methods reveals that the problem can be treated in such a generality that the entries of coefficient matrices are allowed to belong to any complete metric field. The concepts of transformable and strongly transformable groups of matrices are introduced, and these concepts enable us to derive efficient conditions for determining what matrix groups have the required property. 相似文献
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We considered a semilinear, second order periodic system. We assumed that the differential operator x→−x″−Ax has zero as an eigenvalue and has no negative eigenvalues. Also we imposed a strong resonance condition (with respect to the zero eigenvalue) on the potential function F(t,x). Using the second deformation theorem, we established the existence of at least two nontrivial solutions. To do this we needed to conduct a detailed analysis of the Cerami compactness condition, which is actually of independent interest. 相似文献
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Philippe Cieutat 《Journal of Differential Equations》2003,190(1):108-130
We study some properties of bounded and almost periodic solutions of convex Lagrangian systems in the presence of almost periodic forcing
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This paper is devoted to impulsive periodic Gause-type predator-prey systems with monotonic or non-monotonic numerical responses. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones. 相似文献
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In this paper, we study topological properties of semidynamical systems whose continuous dynamics are interrupted by abrupt changes of state. First, we establish results which relate various concepts as stability of Lyapunov, weakly almost periodic motions, recurrence and minimality. In the sequel, we study the stability of Zhukovskij for impulsive systems and we obtain some results about uniform attractors. 相似文献
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Hermano Frid 《Bulletin of the Brazilian Mathematical Society》2001,32(1):1-35
In this paper we survey recent results on the decay of periodic and almost periodic solutions of conservation laws. We also recall some recent results on the global existence of periodic solutions of conservation laws systems which lie inBV
loc
and are constructed through Glimm scheme. The latter motivates a discussion on a possible strategy for solving the open problem of the global existence of periodic solutions of the Euler equations for nonisentropic gas dynamics. We base our decay analysis on a general result about space-time functions which are almost periodic in the space variable, established here for the first time. This result is an abstract version of Theorem 2.1 in [31], which in turn is an extention of the combined result given by Theorems 3.1–3.2 in [9]. 相似文献
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This paper investigates the existence of periodic solutions for an impulsive semi-ratio-dependent predator–prey system with most popular prey-dependent (monotone or non-monotone) and predator-dependent functional response. Sharp sufficient conditions are derived by the invariance property of homotopy and analysis technique. The presented criteria improve and extend many previous results in the literature. 相似文献
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Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays
Valéry Covachev Zlatinka Covacheva Haydar Akça Eada Ahmed Al-Zahrani 《Central European Journal of Mathematics》2003,1(3):292-314
A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant
by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated
ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it
is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2004,57(4):633-637
In this paper we investigate the existence and uniqueness of periodic and almost periodic solution of the differential equation with reflection of argument. The relationship between modules of forced term and solution of the equation is considered. 相似文献
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Carl E Langenhop 《Journal of Differential Equations》1985,58(3):391-403
Conditions are given which guarantee that if T > 0 is sufficiently small, then x(t) = ∝0∞ [dE(s)] x(t — s)+ f(t) has a unique T-periodic solution x for each continuous T-periodic function f. The vectors x and f are n-dimensional; the matrix function E(s) is n × n with bounded total variation. The proof adapts readily to provide an analogous result when x and f are almost periodic functions whose non-zero Fourier frequencies are bounded away from zero. The results are applied to study certain perturbations of the above equation. 相似文献