Theory and Modern Applications
Page 97 of 98
We consider the pair of second-order dynamic equations, (r(t)(xΔ) γ )Δ + p(t)x γ (t) = 0 and (r(t)(xΔ) γ )Δ +
We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Δ4y i = λai+2yi+2, -1≤i≤n-2, y0 = Δ2y-1 = Δy n ...
We reconsider the basic formulation of second-order, two-point, Sturm-Liouville-type boundary value problems on time scales. Although this topic has received extensive attention in recent years, we present som...
We consider the equation (r(t)(yΔ(t))
γ
)Δ + f(t, x(δ(t))) = 0,
, where y(t) = x(t) + p(t)x(τ(t)) and
We construct invariant foliations of the extended state space for nonautonomous semilinear dynamic equations on measure chains (time scales). These equations allow a specific parameter dependence which is the ...
Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δx(n)+q1(n)x μ (n+1) = q2(n)x λ (n+1)+e(n
The existence of a Lyapunov function is established following a method of Yoshizawa for the uniform exponential asymptotic stability of the zero solution of a nonautonomous linear dynamical equation on a time ...
Difference schemes for two-point boundary value problems for systems of first-order nonlinear ordinary differential equations are considered. It was shown in former papers of the authors that starting from the...
We are concerned with proving the existence of one or more than one positive solution of an n-point right-focal boundary value problem for the nonlinear dynamic equation
...
We study a certain singular second-order m-point boundary value problem on a time scale and establish the existence of a solution. The proof of our main result is based upon the Leray-Schauder continuation theore...
We show that two recently discovered q-discrete Painlevé equations are one and the same system. Moreover we provide a novel derivation of this q-discrete system based on transformations obtained with the help of ...
The aim of this paper is to discuss the oscillatory behavior of difference systems of mixed type. Several criteria for oscillations are obtained. Particular results are included in regard to scalar equations.
We investigate the boundedness and asymptotic behavior of a first-order neutral delay dynamic equation on arbitrary time scales, extending some results from difference equations.
The purpose of this contribution is to develop a method for construction of solutions of linear discrete systems with constant coefficients and with pure delay. Solutions are expressed with the aid of a specia...
We present criteria of Hille-Nehari-type for the linear dynamic equation (r(t)yΔ)Δ + p(t)y σ = 0, that is, the criteria in terms of the limit behavior of ...
We discuss the existence of oscillatory and nonoscillatory solutions for first-order impulsive dynamic equations on time scales with certain restrictions on the points of impulse. We will rely on the nonlinear...
The author studies the boundary value problems with p-Laplacian functional difference equation Δφ p (Δx(t)) + r(t)f(x t ) = 0, t ∈ [0, N], x0 =
We discuss the discretizations of the second-order linear ordinary diffrential equations with constant coefficients. Special attention is given to the exact discretization because there exists a difference equ...
We study the theory of Sobolev's spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolev's spaces of func...
We discuss conditions for the existence of at least one positive solution to a nonlinear second-order Sturm-Liouville-type multipoint eigenvalue problem on time scales. The results extend previous work on both...
Essentially nonlinear difference equations in a Euclidean space are considered. Conditions for the existence of periodic solutions and solution estimates are derived. Our main tool is a combined usage of the r...
We provide a maximum norm analysis of an overlapping Schwarz method on nonmatching grids for second-order elliptic obstacle problem. We consider a domain which is the union of two overlapping subdomains where ...
A general method for solving boundary value problems associated to functional difference systems on the discrete half-line is presented and applied in studying the existence of positive unbounded solutions for...
Using exponential dichotomies, we get maximal regularity for retarded functional difference equations. Applications on Volterra difference equations with infinite delay are shown.
We consider the reliability of some numerical methods in preserving the stability properties of the linear stochastic functional differential equation
For a delay difference equation
, g
k
(n) ≤ n, K > 0, a connection between oscillation properties of this equa...
Linear neutral, and especially non-neutral, Volterra difference equations with infinite delay are considered and some new results on the behavior of solutions are established. The results are obtained by the u...
We prove that all solutions to the nonlinear second-order difference equation in integers yn+1 = ⌈ay n ⌉-yn-1, {a ∈ ℝ:|a|<2, a≠0,±1}, y0, y1 ∈ ℤ, are periodic. The first-order sy...
We first give conditions which guarantee that every solution of a first order linear delay dynamic equation for isolated time scales vanishes at infinity. Several interesting examples are given. In the last ha...
We study a discrete time model of the growth of two species of plankton with competitive and allelopathic effects on each other N1(k+1) = N1(k)exp{r1(k)-a11(k)N1(k)-a12(k)N2(k)-b1(k)N1(k)N2(k)}, N2(k+1) = N2(k)ex...
Nonoscillatory solutions of a nonlinear neutral type higher order difference equations are classified by means of their asymptotic behaviors. By means of the Kranoselskii's fixed point theorem, existence crite...
This paper deals with some classes of nonlinear implicit difference equations obtained via discretization of nonlinear differential-algebraic or partial differential-algebraic equations. The unique solvability...
We study the global asymptotic behavior of the positive solutions of the system of rational difference equations xn+1 = f(x n ,yn-k), yn+1 = f(y n ...
The classical theory of homogeneous and inhomogeneous linear difference equations with constant coefficients on the set of integers or nonnegative integers provides effective solution methods for a wide class ...
A method for determination and two methods for approximation of the domain of attraction D a (0) of the asymptotically stable zero steady state of an autonomous, ℝ-analytical, di...
We investigate the functional equation with generalized dilation in the special weighted functional spaces. We provide some sufficient conditions for the existence of the inversion operator in the same form an...
This paper deals with monotone finite difference iterative algorithms for solving nonlinear singularly perturbed reaction-diffusion problems of elliptic and parabolic types. Monotone domain decomposition algor...
We study the third-order linear difference equation with quasi-differences and its adjoint equation. The main results of the paper describe relationships between the oscillatory and nonoscillatory solutions of...
The study of the stability properties of numerical methods leads to considering linear difference equations depending on a complex parameter q. Essentially, the associated characteristic polynomial must have cons...
The main purpose of the paper is to give discrete time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems. In the continuous-time version, these results go ba...
We apply a cone-theoretic fixed point theorem to study the existence of positive periodic solutions of the nonlinear system of functional difference equations x(n+1) = A(n)x(n) + f(n,x n ...
, related to a family of elliptic quartics in the plane
We continue the study of algebraic difference equations of the type un+2u n = ψ(un+1), which started in a previous paper. Here we study the case where the algebraic curves relat...
We establish some new criteria for the oscillation of third-order difference equations of the form
, where Δ is the forward difference operator ...
We prove that if there exists α ≤ β, a pair of lower and upper solutions of the first-order discrete periodic problem Δu(n) = f(n,u(n));n ∈ I N ≡ {0,...,N-1},u(0) = u(N), with f
A discrete-time delayed diffusion model governed by backward difference equations is investigated. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily ...
We investigate the asymptotic behavior of the recursive difference equation yn+1 = (α+βy n )/(1+yn-1) when the parameters α < 0 and β ∈ ℝ. In particular, we establish the bounded...
We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models possessing energy conservation, energy ...
Based on the fixed-point index theory for a Banach space, positive periodic solutions are found for a system of delay difference equations. By using such results, the existence of nontrivial periodic solutions...
We present new existence results for singular discrete initial and boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
Let X be a Banach space over the field ℝ or ℂ, a1,...,a p ∈ ℂ, and (b n )n≥0) a sequence in X. We investigate the Hyers-Ulam stability of the l...
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