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Asymptotic dichotomy for nonoscillatory solutions of a nonlinear difference equation

100%
Zhang G., Cheng S. S.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 4
393-399
EN
A nonlinear difference equation involving the maximum function is studied. We derive sufficient conditions in order that eventually positive or eventually negative solutions tend to zero or to positive or negative infinity.
2
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Unbounded solutions of the max-type difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\} $$

100%
Kerbert C., Radin M.
Open Mathematics
|
2008
|
tom 6
|
nr 2
307-324
EN
We investigate the boundedness nature of positive solutions of the difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\},n = 0,1,..., $$ where {A n}n=0∞ and {B n}n=0∞ are periodic sequences of positive real numbers.
3
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Fonctions zêta d'Igusa et fonctions hypergéométriques

100%
Dan N.
Annales Polonici Mathematici
|
1999
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tom 71
|
nr 1
61-86
FR
On étudie la fonction zêta d'Igusa ζ(P,s) associée à une hypersurface projective complexe {P = 0}. On montre qu'elle est une intégrale d'Euler généralisée et on précise le système différentiel A-hypergéométrique qu'elle satisfait. On indique un algorithme pour la détermination explicite d'une équation aux différences satisfaite par ζ(P,s). On calcule explicitement cette fonction pour quelques cas particuliers. On prouve que la fonction zêta associée au résultant $R_{(1,2)}$ n'est pas une somme de produits de fonctions exponentielles et gamma.
4
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Asymptotic behaviour of solutions of difference equations in Banach spaces

88%
Kisiołek A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2008
|
tom 28
|
nr 1
5-13
EN
In this paper we consider the first order difference equation in a Banach space $Δx_{n} = ∑_{i=0}^∞ a^{i}_{n} f(x_{n+i})$. We show that this equation has a solution asymptotically equal to a. As an application of our result we study the difference equation $Δx_{n} = ∑_{i=0}^∞ a^i_{n}g(x_{n+i}) + ∑_{i=0}^∞ b^{i}_{n}h(x_{n+i}) + y_{n}$ and give conditions when this equation has solutions. In this note we extend the results from [8,9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness and measure of weak noncompactness.
5
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The law of large numbers and a functional equation

88%
Sablik M.
Annales Polonici Mathematici
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1998
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tom 68
|
nr 2
165-175
EN
We deal with the linear functional equation (E) $g(x) = ∑^r_{i=1} p_i g(c_i x)$, where g:(0,∞) → (0,∞) is unknown, $(p₁,...,p_r)$ is a probability distribution, and $c_i$'s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli's Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.
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