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

SHIRIN  MIR; MOHAMMAD BAGHER  GHAEMI; GHASEM ALIZADEH  AFROUZI

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

Authors

SHIRIN MIR Department of Mathematics, Faculty of Sciences, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran
MOHAMMAD BAGHER GHAEMI Department of Mathematics, Faculty of Mathematics Sciences, University of Science and Technology, Tehran, Iran
GHASEM ALIZADEH 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.