Relaxation and weak solutions of nonlocal semilinear evolution systems

Abstract

Abstract We give a relatively short proof of the fact that the solution set of a nonlocal semilinear differential inclusion is dense in the weak solution set of the corresponding convexified system. Moreover, we prove a similar result for the solutions with continuous pseudoderivatives when the right-hand side is continuous with nonempty convex closed and bounded values.

Keywords

• Nonlocal problems
• Weak solutions
• Density