Controllability of partial differential inclusions depending on a parameter and distributed parameter control processes

Let Λ be a topological space and let F be a multifunction from [0,a]x[0,b]x( R n ) 4 xΛ into R n . In this paper we prove that, under suitable assumptions, the set of all λ in Λ such that the partial differential inclusion is locally controllable around the origin of R n at the point (a,b) (resp. R n -completely controllable) is open in Λ . Next, we present an application to the study of two kinds of controllability for the distribuited parameter control process.