Coupled systems of nonlinear variational inequalities and applications?

In this paper we investigate the existence of solutions for a system consisting of two inequalities of variational type. Each inequality is formulated in terms of a nonlinear functional chi and psi, respectively and a coupling functional B. We consider two sets of assumptions (Hi chi ), (Hj psi ) and (HkB), i ,j , k is an element of {1 , 2} and we show that, if the constraints sets are bounded, then a solution exists regardless if we assumed the first or the second hypothesis on chi, psi or B , thus obtaining eight possibilities. When the constraint sets are unbounded a coercivity condition is needed to ensure the existence of solutions. We provide two such conditions. An application, arising from Contact Mechanics, in the form of a partial differential inclusion driven by the phi-Laplace operator is presented in the last section. (c) 2022 Elsevier B.V. All rights reserved.