Wszystkie pola: differential integrals - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Differential inclusions and multivalued integrals
Autorzy:: Cichoń, Kinga
Cichoń, Mieczysław
Satco, Bianca
Powiązania:: https://bibliotekanauki.pl/articles/729320.pdf
Data publikacji:: 2013
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: nonlocal Cauchy problem
Aumann integrals
Pettis integrals
Henstock-Kurzweil-Pettis integrals
measure of weak noncompactness
Opis:: In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces
x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I.
Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented by a short survey about multivalued integration including Pettis and Henstock-Kurzweil-Pettis multivalued integrals.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 171-191
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Integro-differential equations on time scales with Henstock-Kurzweil delta integrals
Autorzy:: Sikorska-Nowak, Aneta
Powiązania:: https://bibliotekanauki.pl/articles/729234.pdf
Data publikacji:: 2011
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: integro-differential equations
nonlinear Volterra integral equation
time scales
Henstock-Kurzweil delta integral
HL delta integral
Banach space
fixed point
measure of noncompactness
Carathéodory solutions
Opis:: In this paper we prove existence theorems for integro - differential equations
$x^Δ (t) = f(t,x(t),∫₀^t k(t,s,x(s))Δs)$,
t ∈ Iₐ = [0,a] ∩ T, a ∈ R₊,
x(0) = x₀
where T denotes a time scale (nonempty closed subset of real numbers R), Iₐ is a time scale interval. Functions f,k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral.
Additionally, functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. Moreover, we prove an Ambrosetti type lemma on a time scale.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 1; 71-90
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Retarded functional differential equations in Banach spaces and Henstock-Kurzweil-Pettis integrals
Autorzy:: Sikorska-Nowak, A.
Powiązania:: https://bibliotekanauki.pl/articles/729411.pdf
Data publikacji:: 2007
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: pseudo-solution
Pettis integral
Henstock-Kurzweil integral
Henstock-Kurzweil-Pettis integral
Cauchy problem
Opis:: We prove an existence theorem for the equation x' = f(t,xₜ), x(Θ) = φ(Θ), where xₜ(Θ) = x(t+Θ), for -r ≤ Θ < 0, t ∈ Iₐ, Iₐ = [0,a], a ∈ R₊ in a Banach space, using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of the measure of weak noncompactness.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 315-327
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

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