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Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints
Sergiu Aizicovici, Ohio University, Athens, OH, Nikolaos S. Papageorgiou, National Technical University, Athens, Greece, and Vasile Staicu, University of Aveiro, Portugal

Memoirs of the American Mathematical Society
2008; 70 pp; softcover
Volume: 196
ISBN-10: 0-8218-4192-0
ISBN-13: 978-0-8218-4192-1
List Price: US$65
Individual Members: US$39
Institutional Members: US$52
Order Code: MEMO/196/915
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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 (variational-hemivariational inequalities). They also prove a multiplicity result for a nonlinear elliptic equation driven by the p-Laplacian 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
  • Variational-hemivariational inequalities
  • Hemivariational inequalities with an asymmetric subdifferential
  • Bibliography
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