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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
Vasile Staicu University of Aveiro, Aveiro, Portugal
Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints
eBook ISBN:  978-1-4704-0521-2
Product Code:  MEMO/196/915.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $39.00
Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints
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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
Vasile Staicu University of Aveiro, Aveiro, Portugal
eBook ISBN:  978-1-4704-0521-2
Product Code:  MEMO/196/915.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $39.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1962008; 70 pp
    MSC: Primary 35;

    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
     
     
    • Chapters
    • 1. Introduction
    • 2. Mathematical background
    • 3. Degree theoretic results
    • 4. Variational-hemivariational inequalities
    • 5. Hemivariational inequalities with an asymmetric subdifferential
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1962008; 70 pp
MSC: Primary 35;

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 \(-\infty\).

  • Chapters
  • 1. Introduction
  • 2. Mathematical background
  • 3. Degree theoretic results
  • 4. Variational-hemivariational inequalities
  • 5. Hemivariational inequalities with an asymmetric subdifferential
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.