Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints
Author： Sergiu Aizicovici;Nikolaos S. Papageorgiou;Vasile Staicu
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470405212
P-ISBN(Paperback): 9780821841921
P-ISBN(Hardback): 9780821841921
Subject： O175.25 Elliptic Equations
Keyword： Differential Equations
Language： ENG
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Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints
Description
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 $-\infty$.