Bibliographic Details
| Title: |
RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES AND HENSTOCK-KURZWEIL-PETTIS INTEGRALS. |
| Authors: |
Sikorska-Nowak, A.1 anetas@amu.edu.pl |
| Source: |
Discussiones Mathematicae: Differential Inclusions, Control & Optimization. 2007, Vol. 27 Issue 2, p315-327. 13p. |
| Subjects: |
Banach spaces, Integral theorems, Mathematical variables, Differential equations, Mathematics education |
| Abstract: |
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 ϵ Ia, Ia = [0, a] a ϵ 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
