Hemivariational inequalities with functions fulfilling directional growth condition

Abstract

The subject of the paper is to establish some existence results for hemivariational inequalities in vector-valued function spaces. A new class of directional growth conditions generalizing the well known sign condition is introduced. The method employed is based on the finite dimensional regularization combined with the Brouwer's fixed point theorem, the Dunford-Pettis compactness criterion in the L¹–space and the finite intersection propertry. The approach includes existence results in the coercive case to Pangiotopoulos. Some applications to differential equations with discontnuous nonlinearities are given.

Keywords:

• Hemivariational inequality
• directional growth condition
• discontinuous nonlinearity

Additional information

Notes on contributors

Zdzislaw Naniewicz