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Boundary Value Problems

, 2006:87483 | Cite as

Existence results for classes of Open image in new window -Laplacian semipositone equations

  • Shobha Oruganti
  • R Shivaji
Open Access
Research Article

Abstract

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

Keywords

Differential Equation Partial Differential Equation Ordinary Differential Equation Positive Constant Functional Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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.

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceThe Behrend CollegeErieUSA
  2. 2.Department of Mathematics and StatisticsMississippi State UniversityMississippi StateUSA

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