BV solutions of a convex sweeping process with a composed perturbation

<p style='text-indent:20px;'>A measurable sweeping process with a composed perturbation is considered in separable Hilbert space. The values of the moving set generating are closed, convex sets. retraction bounded by positive Radon measure. sum two multivalued mappings. first one bounded, not necessarily It time variable, Lipschitz continuous phase and satisfies conventional growth condition. second convex, We assume that this mapping has closed respect to variable graph.</p><p style='text-indent:20px;'>The remaining assumptions concern intersection defined conditions. suppose selector certain compactness properties.</p><p style='text-indent:20px;'>We prove existence solutions for our inclusion. proof based on author's theorem parameter selectors passing through fixed points contraction maps nonconvex, decomposable depending parameter, classical Ky Fan point theorem. results which we obtain new.</p>