On an infinite-dimensional differential equation in vector distributions with discontinuous regular functions on the right hand side.(English)Zbl 0854.34009

The results of the author’s paper [Math. Notes 58, No. 1, 685-691 (1995); translation from Mat. Zametki 58, No. 1, 12-21 (1995; Zbl 0854.34008, see the preceding review)] are extended to the case of differential equations in a Hilbert space $$H$$ of the form $\dot x(t)= Ax(t)+ f(x, u, t)+ \beta(x, u, t) b(x, u, t) \dot u(t),\;x(t_0)= x_0,$ where $$A$$ is a generator of a $$C_0$$-semigroup, $$f$$ is a bounded continuous function, $$b(x, u, t)(\cdot)$$ is a linear continuous operator and $$\beta$$ is a scalar piecewise continuous function.

MSC:

 34A37 Ordinary differential equations with impulses 34G20 Nonlinear differential equations in abstract spaces 34K30 Functional-differential equations in abstract spaces

Zbl 0854.34008
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