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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

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On generalized Laplace equation and nonlinear operators

Corneliu Udrea
  • Mathematics Department, Faculty of Mathematics and Computer Science, University of Piteşti, Târgu din Vale Street, No. 1, 110040 Piteşti, România
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Published Online: 2012-01-19 | DOI: https://doi.org/10.1515/apam.2011.009


This work deals with nonlinear potential theory, particularly with the techniques of the construction of nonlinear resolvent associated with a given nonlinear operator. The first section is devoted to the theoretical case. After making some introductory remarks about the Dirichlet problem for the generalized Laplace equation, we define a nonlinear operator on the space of essentially bounded functions on an open bounded subset of k-dimensional real space and we associate with it a sub-Markovian nonlinear resolvent.

Keywords.: Nonlinear potential theory; complete maximum principle; resolvents

About the article

Received: 2010-09-22

Accepted: 2011-04-25

Published Online: 2012-01-19

Published in Print: 2012-01-01

Citation Information: Advances in Pure and Applied Mathematics, Volume 3, Issue 1, Pages 45–57, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2011.009.

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