AN EXISTENCE THEOREM FOR A CLASS OF DIFFERENTIAL INCLUSIONS WITH A PRECISE ESTIMATE ON THE GRADIENT OF A SOLUTION

S. Mir; M. B. Ghaemi; G. A.  Afrouzi

AN EXISTENCE THEOREM FOR A CLASS OF DIFFERENTIAL INCLUSIONS WITH A PRECISE ESTIMATE ON THE GRADIENT OF A SOLUTION

Authors

S. Mir Department of Mathematics, Faculty of Sciences, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran
M. B. Ghaemi Department of Mathematics, Faculty of Mathematics Sciences, University of Science and Technology, Tehran, Iran
G. A. Afrouzi Department of Mathematics, Faculty of Mathematics Sciences, University of Mazandaran, Babolsar, Iran

Keywords:

locally Lipschitz functions, differential inclusions, uniqueness, local minimum

Abstract

In this paper, by using nonsmooth version of very recently theorem of Ricceri relating to continuously functionals, we get a new class of nonlinearities for which the Dirichlet problem has a solution, with a precise estimate on the gradient.