Document Zbl 0962.34043

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Kubiaczyk, Ireneusz; Sikorska, Aneta

Differential equations in Banach space and Henstock-Kurzweil integrals. (English) Zbl 0962.34043

Discuss. Math., Differ. Incl. 19, No. 1-2, 35-43 (1999).

The authors establish the existence of solutions to the differential equation \(x'(t)= f(t, x(t))\) in a Banach space, under the key condition that \(f\) is Henstock-Kurzweil integrable. The theory is generalized to abstract differential inclusions.

Reviewer: Sergiu Aizicovici (Athens/Ohio)

Cited in 4 Documents

MSC:

34G20	Nonlinear differential equations in abstract spaces
34A60	Ordinary differential inclusions

Keywords:

Henstock-Kurzweil integrals; existence; solutions; abstract differential inclusions

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