Method of averaging for the system of functional-differential inclusions

Teresa Janiak; Elżbieta Łuczak-Kumorek

Displaying similar documents to “Method of averaging for the system of functional-differential inclusions”

Continuous solutions of the functional equation $φ (f (x)) = G (x, φ (x))$ for vector-valued functions φ

Z. Krzeszowiak (1969)

Annales Polonici Mathematici

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The functional equation $f^{2} (x) = g (x)$

James C. Lillo (1967)

Annales Polonici Mathematici

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$C^{r}$ -solutions of a system of functional equations

Z. Kominek (1974)

Annales Polonici Mathematici

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On the functional equation $f (x) + \sum_{i = 1}^{n} g_{i} (y_{i}) = h (T (x, y_{1}, y_{2}, . . ., y_{n}))$

C. T. Ng (1973)

Annales Polonici Mathematici

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On some symmetrical equations of the form $f_{1} (x_{1} + . . . + x_{n}) = \sum_{i_{1}, . . ., i_{n}}) f_{1} (x_{i} 1) . . . f_{n} (x_{i} n)$

H. Światak (1967)

Annales Polonici Mathematici

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On the solutions of the functional equation $ϕ (x) + ϕ^{2} (x) = F (x)$

M. Malenica (1982)

Matematički Vesnik

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Second order quasilinear functional evolution equations

László Simon (2015)

Mathematica Bohemica

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We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in $(0, T)$ is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in $(0, \infty)$ (boundedness and stabilization as $t \to \infty$ ) are shown.

Solutions for the p-order Feigenbaum’s functional equation $h (g (x)) = g^{p} (h (x))$

Min Zhang, Jianguo Si (2014)

Annales Polonici Mathematici

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This work deals with Feigenbaum’s functional equation ⎧ $h (g (x)) = g^{p} (h (x))$ , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, $g^{p}$ is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.

On Probability Distribution Solutions of a Functional Equation

Janusz Morawiec, Ludwig Reich (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let 0 < β < α < 1 and let p ∈ (0,1). We consider the functional equation φ(x) = pφ (x-β)/(1-β) + (1-p)φ(minx/α, (x(α-β)+β(1-α))/α(1-β)) and its solutions in two classes of functions, namely ℐ = φ: ℝ → ℝ|φ is increasing, ${φ |}_{(- \infty, 0]} = 0$ , ${φ |}_{[1, \infty)} = 1$ , = φ: ℝ → ℝ|φ is continuous, ${φ |}_{(- \infty, 0]} = 0$ , ${φ |}_{[1, \infty)} = 1$ . We prove that the above equation has at most one solution in and that for some parameters α,β and p such a solution exists, and for some it does not. We also determine all solutions of the equation in ℐ and we show the...

A useful algebra for functional calculus

Mohammed Hemdaoui (2019)

Mathematica Bohemica

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We show that some unital complex commutative LF-algebra of $𝒞^{(\infty)}$ $ℕ$ -tempered functions on $ℝ^{+}$ (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.

The law of large numbers and a functional equation

Maciej Sablik (1998)

Annales Polonici Mathematici

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We deal with the linear functional equation (E) $g (x) = \sum_{i = 1}^{r} p_{i} g (c_{i} x)$ , where g:(0,∞) → (0,∞) is unknown, $(p ₁, . . ., p_{r})$ 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.

On the Functional Equation $f (λ) + f (ω λ) f (ω^{- 1} λ) = 1$ , $(ω^{5} = 1)$

Yasutaka Sibuya (1984)

Recherche Coopérative sur Programme n°25

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The existence of Carathéodory solutions of hyperbolic functional differential equations

Adrian Karpowicz (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We consider the following Darboux problem for the functional differential equation $\partial ² u / \partial x \partial y (x, y) = f (x, y, u_{(x, y)}, \partial u / \partial x (x, y), \partial u / \partial y (x, y))$ a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b] $0, a] \times (0, b],$ where the function $u_{(x, y)} : [- a ₀, 0] \times [- b ₀, 0] \to ℝ^{k}$ is defined by $u_{(x, y)} (s, t) = u (s + x, t + y)$ for (s,t) ∈ [-a₀,0]×[-b₀,0]. We prove a theorem on existence of the Carathéodory solutions of the above problem.

Cauchy-like functional equation based on a class of uninorms

Feng Qin (2015)

Kybernetika

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Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. In the case of bisymmetric aggregation operators with the neutral elements, Saminger, Mesiar and Dubois, already reduced characterization of commuting $n$ -ary operators to resolving the unary distributive functional equations. And then the full characterizations of these equations are obtained under the assumption that...