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Boundary Value Problems
Boundary Value Problems Cover Image
  • Research Article
  • Open Access

Existence results for classes of -Laplacian semipositone equations

Boundary Value Problems20062006:87483

https://doi.org/10.1155/BVP/2006/87483

©  S. Oruganti and R. Shivaji 2006

  • Received: 22 September 2005
  • Accepted: 10 November 2005
  • Published:

Abstract

We study positive solutions to classes of boundary value problems of the form in on , where denotes the -Laplacian operator defined by ; , is a parameter, is a bounded domain in ; with of class and connected (if , we assume that is a bounded open interval), and for some (semipositone problems). In particular, we first study the case when where is a parameter and is a function such that , for and for . We establish positive constants and such that the above equation has a positive solution when and . Next we study the case when (logistic equation with constant yield harvesting) where and is a function that is allowed to be negative near the boundary of . Here is a function satisfying for , , and . We establish a positive constant such that the above equation has a positive solution when Our proofs are based on subsuper solution techniques.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Positive Constant
  • Functional Equation

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Authors’ Affiliations

(1)
Department of Mathematics, School of Science, The Behrend College, Penn State Erie, Erie, PA 16563, USA
(2)
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA

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Copyright

© S. Oruganti and R. Shivaji 2006

This article is published under license to BioMed Central Ltd. 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.

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