2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160657In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is in relation with the valuation of firms in a financial market.19 pagesProbabilityOptimization and Control60G40 ; 62P20 ; 91B99 ; 91B28 ; 35B37 ; 49L25.text