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1
Content available On existence and global attractivity of periodic solutions of nonlinear delay differential equations
Qian Chuanxi, Smith Justin
Opuscula Mathematica
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2019
|
Vol. 39, no. 6
839--862
EN
onsider the delay differential equation with a forcing term [formula] (*) where ƒ (t, x) : [0,) x [0, ∞) —> R, g(t, x) : [0, ∞) x [0, ∞) —> [0, ∞) are continuous functions and w-periodic in t, r(t) : [0, ∞) —> R is a continuous function and r ∈ (0, ∞) is a positive constant. We first obtain a sufficient condition for the existence of a unique nonnegative periodic solution [formula] of the associated unforced differential equation of Eq. (*) [formula] (**) Then we obtain a sufficient condition so that every nonnegative solution of the forced equation (*) converges to this nonnegative periodic solution [formula] of the associated unforced equation (**). Applications from mathematical biology and numerical examples are also given.
2
Content available The second Cushing-Henson conjecture for the beverton holt q-difference equation
Bohner M., Streipert S. H.
Opuscula Mathematica
|
2017
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Vol. 37, no. 6
795--819
EN
In this paper, we study the second Cushing-Henson conjecture for the Beverton-Holt difference equation with periodic inherent growth rate and periodic carrying capacity in the quantum calculus setting. We give a short summary of recent results regarding the Beverton-Holt difference and Q-difference equation and introduce the theory of quantum calculus briefly. Next, we analyze the second Cushing-Henson conjecture. We extend recent studies in [The Beverton-Holt q-difference equation with periodic growth rate, Difference Equations, Discrete Dynamical Systems, and Applications, Springer-Verlag, Berlin, Heidelberg, New York, 2015, pp. 3-14] and state a modified formulation of the second Cushing-Henson conjecture for the Beverton-Holt Q-difference equation as a generalization of existing formulations.
3
Content available remote Global behavior of higher order a rational difference equation
Elabbasy E.M., Eleissawy S M
Fasciculi Mathematici
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2014
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Nr 53
39--52
EN
The main objective of this paper is to study the global asymptotic stability and the periodic character of the rational difference equation …[wzór], n – 0,1,…, where the parameters a, β, ϒ, p, q are nonnegative real numbers and initial conditions are nonnegative real numbers l, r, k are nonnegative integers, such that l < k and r < k. Also, we give some numerical simulations to the equation to illustrate our results.
4
Content available Periodic solutions in multivariate invariance arguments
Chudziak J., Wójcik S.
Opuscula Mathematica
|
2013
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Vol. 33, no. 3
455--465
EN
Inspired by the recent results of A.E. Abbas we determine continuous multivariate utility functions invariant with respect to a wide family of transformations related to the shift transformations.
5
Content available Existence of periodic solutions for totally nonlinear neutral differential equations with functional delay
Yankson E.
Opuscula Mathematica
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2012
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Vol. 32, no. 3
617-627
6
Content available remote Periodic solutions for highly nonlinear oscillation systems
Ghadimi M., Barari A., Kaliji H. D., Domairry G.
Archives of Civil and Mechanical Engineering
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2012
|
Vol. 12, no. 3
389--395
EN
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams. The results obtained are compared with Variational Iteration Method (VIM) and other analytical methods as well as time marching solution. The results given show the effectiveness and accuracy of the proposed techniques.
7
Content available remote Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays
Zhang Q., Yang L., Liao D.
International Journal of Applied Mathematics and Computer Science
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2011
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Vol. 21, no 4
649-658
EN
Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.
8
Content available remote Positive periodic solutions for second order impulsive differential equations
Shen J., Wang W., He Z.
Demonstratio Mathematica
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2011
|
Vol. 44, nr 2
297-316
EN
The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using fixed point theorem in cone, new existence results of positive periodic solutions are obtained without assuming the existence of positive periodic solutions of the corresponding continuous equation.
9
Content available remote On the solutions of a rational system of difference equations
Elsayed E. M.
Fasciculi Mathematici
|
2010
|
Nr 45
25-36
EN
In this paper we deal with the solutions of the system of the difference equations xn+1 = ...[wzór], yn+1 = ...[wzór], with a nonzero real numbers initial conditions.
10
Content available remote On the solution of the recursive sequence
Elabbasy E.M., Elsayed E.M.
Fasciculi Mathematici
|
2009
|
Nr 41
55-63
EN
We obtain in this paper the solution of the following recursive sequence where the initial conditions x-2, x-1are arbitrary non zero real numbers.
11
Content available remote Existence and global exponenetial stability of periodic solution of high-order Cohen-Grossberg neural network with impulses
Liu J.
Demonstratio Mathematica
|
2009
|
Vol. 42, nr 2
323-338
EN
Sufficient conditions are obtained for the existence and global exponential stability of periodic solution of high-order Cohen-Grossberg neural network with impulses by using Mawhin's continuation theorem of coincidence degree and by means of a method based differential inequality.
12
Content available remote On the solution of recursive sequence of order two
Elsayed E. M.
Fasciculi Mathematici
|
2008
|
Nr 40
5-13
EN
We obtain in this paper the solution of the following difference equation (formula), n= 0, 1,... where the initial conditions x-1, x0 are arbitrary real numbers.
13
Content available remote Periodic solutions of first-order functional differential equations with supper-linear nonliearities
Liu Y.
Fasciculi Mathematici
|
2007
|
Nr 38
57-74
EN
The existence results for periodic solutions concerning first-order functional differential equation are proved. The methods are based upon the coincidence degree theory by Mawhin. The results obtained are new. Examples, that can not be solved by known theorems, are given to illustrate the main results.
14
Content available remote Convergence and periodic properties of solutions for a class of delay difference equation
Zhu H., Huang L.
Fasciculi Mathematici
|
2007
|
Nr 37
121-128
EN
We propose a class of delay difference equation with piecewise constant nonlinearity. The convergence of solutions and the existence of globally asymptotically stable periodic solutions are investigated for such a class of difference equation.
15
Content available remote Subharmonics of a Hamiltonian systems class
Timoumi M.
Demonstratio Mathematica
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2004
|
Vol. 37, nr 4
977--990
EN
In this note we are interested in the existence of subharmonics of Hamiltonian system x = JH'(t,x), where H is a convex noncoercive Hamiltonian. This type of Hamiltonian systems governs the motion of relativistic particles. The resolution method consists in finding critical points of dual action integral.
16
Content available remote On existence and stability of forced periodic oscillations for a rod in the viscous fluid
Hajdukiewicz M.
Demonstratio Mathematica
|
2004
|
Vol. 37, nr 1
91--100
EN
The paper is devoted to the development of a numerical algorithm for finding the time-periodic transverse oscillations of a rod under external forces. Moreover, the dynamical stablility of these oscillations is proved under damping properities of the fluid.
17
Content available remote Periodic solutions of the Riccati equation in Banach spaces
Baris J., Buraczewski A.
Demonstratio Mathematica
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2003
|
Vol. 36, nr 2
343--353
EN
In this paper we study the problem of the existence and the construction of periodic solutions of the Riccati equation with continuous periodic coefficients denned on the real line with values in Banach space.
18
Content available remote On a radial periodic solution to the diffusion equation for the exterior of a ball
Tal-Figiel B.
Fasciculi Mathematici
|
2002
|
Nr 33
111-114
EN
The subject of the paper is the construction of a periodic radial solution to the diffusion parabolic differential equation (I) delta u(x,t)-D:u(x,t) = f(x,t), where sigma = D(2)(x)+ D(2)(x2)+ D2(x3), x = (xl,x1,x1), t belonge(-infinity, inffinity), in radial coordinates (r,t) (r,[x] r=\x\= (x(2)(1) + x(2)(2) , in the exterion of the ball D(1), = {(r,t):r>R,t (-infinity, infinity)}. Equation (I) is of the from (II) D] (W(r, t)) - D, (W(r, t) = rU (r, t) (r, t). By the suitable Green function (r, t, p, s) -> G(r, t, p, s), we construct the periodic solution with respect to the variable / of equation (II) as the potential W(r, t) of the double layer.
19
Content available remote Periodic solutions of two-species difusion models with continuous time delays
Huo H.-F., Li W.-T., Cheng S. S.
Demonstratio Mathematica
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2002
|
Vol. 35, nr 2
433-446
EN
Two-species prey-predator diffusion models with periodic coefficients and continuous time delays are investigated. We derive sufficient conditions that guarantee the existence of positive periodic solutions which are globally asymptotically stable.
20
Content available remote Periodic solutions for evolution inclusions with time-dependent subdifferentials
Matzakos N., Papageorgiu N. S.
Demonstratio Mathematica
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2002
|
Vol. 35, nr 3
521-538
EN
In this paper we examine a periodic evolution equation driven by a time-dependent subdifferential and with a multivalued forcing term. Using a fixed point theorem for pseudo-acyclic multifunctions we prove the existence of periodic trajectories. This approach requires a study of the structure of the solution set of the Cauchy problem, which is also conducted in this paper.
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