### ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION OF A DIFFERENTIAL EQUATION WITH INTERACTION GOVERNED BY GENERALIZED FUNCTION IN ABSTRACT WIENER SPACE

**VOLODYMYR B. BRAYMAN**

*Theory of Stochastic Processes Vol. 11 (27), no. 3–4, 2005, pp. 29–41*

We consider the following differential equation with interaction governed by a generalized function $\varkappa_0$

$$

\frac{dx(u,t)}{dt}=a(x(u,t),\varkappa_t), \ x(u,0)=u, \ \varkappa_t=\varkappa_0\circ x(\cdot,t)^{-1}.

$$

The conditions that guarantee the existence and uniqueness of a solution when mapping a belongs to some Sobolev space are obtained.

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