# Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints

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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 $-\infty$.