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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Existence theorem for multivalued hyperbolic equation

100%
Kubiaczyk I.
Commentationes Mathematicae
|
1987
|
tom 27
|
nr 1
EN
The article contains no abstract
2
Content available remote

Asymptotic properties of third order functional dynamic equations on time scales

63%
Kubiaczyk I., Saker S.
Annales Polonici Mathematici
|
2011
|
tom 100
|
nr 3
203-222
EN
The purpose of this paper is to study the asymptotic properties of nonoscillatory solutions of the third order nonlinear functional dynamic equation $[p(t)[(r(t)x^{Δ}(t))^{Δ}]^{γ}]^{Δ} + q(t)f(x(τ(t))) = 0$, t ≥ t₀, on a time scale 𝕋, where γ > 0 is a quotient of odd positive integers, and p, q, r and τ are positive right-dense continuous functions defined on 𝕋. We classify the nonoscillatory solutions into certain classes $C_{i}$, i = 0,1,2,3, according to the sign of the Δ-quasi-derivatives and obtain sufficient conditions in order that $C_{i} = ∅$. Also, we establish some sufficient conditions which ensure the property A of the solutions. Our results are new for third order dynamic equations and involve and improve some results previously obtained for differential and difference equations. Some examples are worked out to demonstrate the main results.
3
Content available remote

Oscillation and global attractivity in a discrete survival red blood cells model

63%
Kubiaczyk I., Saker S.
Applicationes Mathematicae
|
2003
|
tom 30
|
nr 4
441-449
EN
We consider the discrete survival red blood cells model (*) $N_{n+1} - Nₙ = -δₙNₙ + Pₙe^{-aN_{n-k}}$, where δₙ and Pₙ are positive sequences. In the autonomous case we show that (*) has a unique positive steady state N*, we establish some sufficient conditions for oscillation of all positive solutions about N*, and when k = 1 we give a sufficient condition for N* to be globally asymptotically stable. In the nonatonomous case, assuming that there exists a positive solution {Nₙ*}, we present necessary and sufficient conditions for oscillation of all positive solutions of (*) about {Nₙ*}. Our results can be considered as discrete analogues of the recent results by Saker and Agarwal [12] and solve an open problem posed by Kocic and Ladas [8].
4
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An existence theorem for the generalized hyperbolic equation \(z''_{xy} \in F(x, y, z)\) in Banach space

63%
Dawidowski M., Kubiaczyk I.
Commentationes Mathematicae
|
1990
|
tom 30
|
nr 1
EN
The article contains no abstract
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