Quasilinear elliptic inclusions of Clarke's gradient type under local growth conditions

Abstract

We consider a class of elliptic inclusions under Dirichlet boundary conditions involving multifunctions of Clarke's generalized gradient that satisfies only a one-sided local growth condition. An appropriate modification of the associated potential function along with truncation techniques will allow us to apply the theory of multivalued pseudomonotone operators for obtaining existence and comparison results under only one-sided local growth conditions on Clarke's generalized gradient.

Keywords:

• Elliptic inclusions
• Clarke's generalized gradient
• Multivalued pseudomonotone operators
• p-Laplacian
• One-sided local growth conditions
• Sub-supersolution

Keywords:

• AMS Subject Classifications: 35J60
• 35R05
• 49J52
• 49J53