Temat: measures of weak noncompactness - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Knesers theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces
Autorzy:: Cichoń, Mieczysław
Kubiaczyk, Ireneusz
Powiązania:: https://bibliotekanauki.pl/articles/1311465.pdf
Data publikacji:: 1995
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: set of solutions
pseudo-solutions
measures of weak noncompactness
Pettis integral
Opis:: We investigate the structure of the set of solutions of the Cauchy problem x' = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in $C_{w}(I,E)$, the space of all continuous functions from I to E endowed with the weak topology. Under some additional assumptions these solutions are, in fact, weak solutions or strong Carathéodory solutions, so we also obtain Kneser-type theorems for these classes of solutions.
Źródło:: Annales Polonici Mathematici; 1995, 62, 1; 13-21
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On theorems for weak solutions of nonlinear differential equations with and without delay in Banach spaces
Autorzy:: Gomaa, Adel Mahmoud
Powiązania:: https://bibliotekanauki.pl/articles/745302.pdf
Data publikacji:: 2007
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Nonlinear differential equations
weak solutions
measures of noncompactness
delay
Opis:: In the present work we give an existence theorem for bounded weak solution of the differential equation \[ \dot{x}(t) = A(t)x(t) + f (t, x(t)),\quad t \geq 0 \] where $\{A(t) : t \in I\mathbb{R}^+ \}$ is a family of linear operators from a Banach space $E$ into itself, $B_r = \{x \in E : \|x\| \leq r\}$ and $f \colon \mathbb{R}^+ \times B_r \to E$ is weakly-weakly continuous. Furthermore, we give existence theorem for the differential equation with delay \[ \dot{x}(t) = \hat{A}(t) x(t) + f^d (t, θ_t x)\quad \text{if}\ t \in [0, T], \] where $T, d \gt 0$, $C_{B_r} ([-d, 0])$ is the Banach space of continuous functions from $[-d, 0]$ into $B_r$, $f_d\colon [0, T] \times C_{B_r} ([-d, 0]) \to E$ weakly-weakly continuous function, $\hat{A}(t)\colon [0,T] \to L(E)$ is strongly measurable and Bochner integrable operator on $[0,T]$ and $θ_t x(s) = x(t + s)$ for all $s \in [-d, 0]$.
Źródło:: Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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