Chapter

Nonlinear Inclusions and Hemivariational Inequalities

Volume 26 of the series Advances in Mechanics and Mathematics pp 95-120

Date:

Stationary Inclusions and Hemivariational Inequalities

  • Stanisław MigórskiAffiliated withFaculty of Mathematics and Computer Science Institute of Computer Science, Jagiellonian University
  • , Anna OchalAffiliated withFaculty of Mathematics and Computer Science Institute of Computer Science, Jagiellonian University
  • , Mircea SofoneaAffiliated withLaboratoire de Mathématiques et Physique (LAMPS), Université de Perpignan Via Domitia

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Abstract

In this chapter we study stationary operator inclusions, i.e., inclusions in which the derivatives of the unknown with respect to the time variable are not involved. We start with a basic existence result for abstract operator inclusions. Then we use it in order to prove the existence of solutions for various operator inclusions of subdifferential type. We also prove that, under additional assumptions, the solution of the corresponding inclusions is unique. Finally, we specialize our existence and uniqueness results in the study of stationary hemivariational inequalities. The theorems presented in this chapter will be applied in the study of static frictional contact problems in Chap. 7.