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Abstract and Applied Analysis
Volume 2004 (2004), Issue 9, Pages 723-727
http://dx.doi.org/10.1155/S1085337504311097

Logistic equation with the p-Laplacian and constant yield harvesting

1Department of Mathematics, School of Science, Penn State Erie, The Behrend College, Penn State University, PA 16563, USA
2Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA
3School of Mathematics, Harbin Normal University, Harbin, Heilongjiang 150080, China
4Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA

Received 29 September 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the positive solutions of a quasilinear elliptic equation with p-Laplacian, logistic-type growth rate function, and a constant yield harvesting. We use sub-super-solution methods to prove the existence of a maximal positive solution when the harvesting rate is under a certain positive constant.