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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
Available Formats:
Electronic 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 Click above image for expanded view 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 Available Formats:  Electronic 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 $-\infty$.

• Chapters
• 1. Introduction
• 2. Mathematical background
• 3. Degree theoretic results
• 4. Variational-hemivariational inequalities
• 5. Hemivariational inequalities with an asymmetric subdifferential
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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
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