Difference equations on R
Difference inequality for stability of impulsive difference equations with distributed delays
... impulsive difference equations with distributed ...delay difference inequality and using the properties of “r-cone” and eigenspace of the spectral radius of non-negative matrices, some new ...
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Transformations of Difference Equations I
... given by permuting the factors S and Q or the factors P and R, that is, by QS or RP , respectively, as in the continuous case. Applying this transformation must then result in a transformed equation of exactly the ...
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Unconditional convergence of difference equations
... ∈ R with {a} ∈ R , that is, in the sequel we consider the fixed injection a → { a } of R into R and we identify R with its ...= R , / = {–∞, ...
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On difference equations concerning Schwarzian equation
... In this paper, we use the basic notions of Nevanlinna theory, such as T(r, f ), m(r, f ), N(r, f ), and so on; see [–]. Let S(r, f ) denote any quantity satisfying S(r, f ) = o(T ...
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Chaotification for linear delay difference equations
... rameters. They showed that the controlled system is chaotic in the sense of Li-Yorke by using the Marotto theorem. However, there exists some problem in their proofs. We state as follows. By the definition of a snap-back ...
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Almost Automorphic Solutions of Difference Equations
... Remark 2.3. Examples of discrete almost automorphic functions which are not discrete almost periodic were first constructed by Veech 39 . In fact, note that the examples introduced in 39 are not on the additive group ...
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Oscillatory difference equations and moment problems
... with initial conditions H q (x) = , H q (x) = αx for all x ∈ R. Note that α is chosen as a fixed positive real number. Here, the number q may range in the set of all positive real numbers, without the number ...
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Partial Differential and Difference Equations
... and our general problem will be to determine sufficient conditions on the ars under which solutions of the difference equations will converge to the solutions of corresponding partial di[r] ...
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On linear Volterra difference equations with infinite delay
... difference equations of convolution type, Proceedings of the Special Program on Dynamical Systems and Ordinary Differential Equations held at the Nankai Insti- tute of Mathematics (Tianjin, 1990/1991) ...
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A functional analytic method for the study of difference equations
... Consider the distribution of heat through a “very long” (so long that it can be labelled by the set of integers) nonuniform thin plate. Let u(i, j, n) be the temperature of the plate at the position (i, j) and time n. At ...
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Hahn difference equations in Banach algebras
... 11. Jackson, FH: On q-functions and a certain difference operator. Trans. R. Soc. Edinb. 46, 253-281 (1908) 12. Bird, MT: On generalizations of sum formulas of the Euler-Maclaurin type. Am. J. Math. 58, 487-503 ...
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Solutions of complex difference and q difference equations
... Second, we will investigate solutions of higher-order complex q-difference equations. The standard logarithmic derivative lemma and Wiman-Valiron theory (see []) play important roles in the study of growth and ...
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Some results on q difference equations
... where the right-hand side is rational in both arguments, has been widely studied during the last decades; see, e.g., [–]. Gundersen et al. [] considered the order of growth of mero- morphic solutions of (.), from ...
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Some new finite difference inequalities arising in the theory of difference equations
... the first variable, while nondecreasing in the second variable. a : I ® I is nondecreas- ing with a (m) ≥ m for ∀ m Î I, while β : I → I is nondecreasing with b (n) ≤ n for ∀n ∈ I . p, q, r, l are defined as in ...
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Classification of solutions of delay difference equations
... & ZHANG, B.G., Oscillation of difference equations with delay, Proceeding of thee Internationa; onference on Theory and Applications of Differential Equations, Ohio University 1988, 257-[r] ...
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Oscillation of nonlinear delay difference equations
... We obtain some oscillation criteria for solutions of the nonlinear delay differ αj ence equation of the form xn+1 − xn + pn m j=1 xn−k = 0.. 2000 Mathematics Subject Classification.[r] ...
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On a class of fourth order nonlinear difference equations
... difference equations. Compared to second-order difference equations, the study of higher-order equations, and in particular fourth-order equations (see, ...difference equations is the ...
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Modelling AIDS epidemic and treatment with difference equations
... in particular for biological systems, bookkeeping constraints, like population counting, introduce a discreteness in the data gathering which must, in principle, be reflected in the model’s equations. Moreover, ...
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On the oscillation of certain third order difference equations
... difference equations of type (1.4;δ), the study of higher-order equations, and in particular third-order equations of type ...for equations with deviating ...
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Sixteen practically solvable systems of difference equations
... In the last two decades the topic re-attracted some interest, although it seems that a considerable part of the results in the topic are not quite original (see, e.g., some of the comments in [15–19]). Nevertheless, the ...
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