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

Logistic equation with the p-Laplacian and constant yield harvesting

Shobha Oruganti,1 Junping Shi,2,3 and Ratnasingham Shivaji4

 1Department of Mathematics, School of Science, Penn State Erie, The Behrend College, Penn State University, 16563, PA, USA
2Department of Mathematics, College of William and Mary, Williamsburg 23187-8795, VA, USA
3School of Mathematics, Harbin Normal University, Harbin, Heilongjiang 150080, China
4Department of Mathematics and Statistics, Mississippi State University, Mississippi State 39762, MS, USA
Received 29 September 2003

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.