## Continuous dependence results for subdifferential inclusions.(English)Zbl 0777.34042

The paper deals with the parametrized class of nonlinear evolution inclusions of subdifferential type (1) $$-\dot x(t)\in\partial\varphi(x(t),\lambda)+F(t,x(t),\lambda)$$ a.e., $$x(0)=x_ 0(\lambda)$$. The author studies continuity properties of the multifunction $$\lambda\to S(\lambda)$$, where $$S(\lambda)$$ is the set of strong solutions of (1). He finds conditions under which the solution set depends continuously on $$L$$ for both the Victoris and Hausdorff topologies. Then, using these interesting results, he studies the variational stability of a class of nonlinear distributed parameter optimal control problems. He also shows how these results incorporate the stability analysis of differential variational inequalities.

### MSC:

 34G20 Nonlinear differential equations in abstract spaces 49J20 Existence theories for optimal control problems involving partial differential equations
Full Text: