Abstract:

This paper deals with the boundary value problems for a class of partial differential inclusions -Δu∈G(x,u). When G(x,u) takes bounded weakly compact convex values,  is measurable about variable x, and is a closed graph about variable u, using the techniques from the KakutaniFan fixed point theory, we have proved the existence theorems of boundary value solutions of the system and the solution sets are weakly compact.

Key words: partial differential inclusion, boundary value solution, fixed point