Topological degree and applications to elliptic problems with discontinuous nonlinearity

Volume 10, Issue 2, pp 612--624 http://dx.doi.org/10.22436/jnsa.010.02.24

Publication Date: February 20, 2017 Submission Date: October 27, 2016

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Authors

In-Sook Kim - Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea.

Abstract

We develop a topological degree theory for a class of locally bounded weakly upper semicontinuous set-valued operators of generalized (\(S_+\)) type in real reflexive separable Banach spaces, based on the Berkovits-Tienari degree. The method of approach is to use elliptic super-regularization by means of certain compact embeddings, instead of the Galerkin method. Applying the degree theory, we tackle an elliptic boundary value problem with discontinuous nonlinearity.

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Keywords

• Set-valued operators of (\(S_+\)) type
• degree theory
• p-Laplacian.

MSC

•  47H04
•  47H05
•  47H11
•  47H30
•  47J05

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