- Tytuł:
- Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals
- Autorzy:
-
Kubiaczyk, Ireneusz
Sikorska-Nowak, Aneta - Powiązania:
- https://bibliotekanauki.pl/articles/729401.pdf
- Data publikacji:
- 2009
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Cauchy dynamic problem
Banach space
measure of noncompactness
Carathéodory's type solutions
time scales
fixed point - Opis:
-
In the paper, we prove the existence of solutions and Carathéodory's type solutions of the dynamic Cauchy problem
$x^Δ(t) = f(t,x(t))$, t ∈ T,
x(0) = x₀,
where T denotes an unbounded time scale (a nonempty closed subset of R and such that there exists a sequence (xₙ) in T and xₙ → ∞) and f is continuous or satisfies Carathéodory's conditions and some conditions expressed in terms of measures of noncompactness. The Sadovskii fixed point theorem and Ambrosetti's lemma are used to prove the main result. The results presented in the paper are new not only for Banach valued functions, but also for real-valued functions. - Źródło:
-
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 113-126
1509-9407 - Pojawia się w:
- Discussiones Mathematicae, Differential Inclusions, Control and Optimization
- Dostawca treści:
- Biblioteka Nauki
Artykuł