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.


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


Zbl 0854.34008
Full Text: DOI EuDML