Memoirs of the American Mathematical Society 2008; 70 pp; softcover Volume: 196 ISBN10: 0821841920 ISBN13: 9780821841921 List Price: US$65 Individual Members: US$39 Institutional Members: US$52 Order Code: MEMO/196/915
 In the first part of this paper, the authors examine the degree map of multivalued perturbations of nonlinear operators of monotone type and prove that at a local minimizer of the corresponding Euler functional, this degree equals one. Then they use this result to prove multiplicity results for certain classes of unilateral problems with nonsmooth potential (variationalhemivariational inequalities). They also prove a multiplicity result for a nonlinear elliptic equation driven by the pLaplacian with a nonsmooth potential (hemivariational inequality) whose subdifferential exhibits an asymmetric asymptotic behavior at \(+\infty\) and \(\infty\). Table of Contents  Introduction
 Mathematical background
 Degree theoretic results
 Variationalhemivariational inequalities
 Hemivariational inequalities with an asymmetric subdifferential
 Bibliography
