## Boundary Value Problems

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# Existence results for classes of -Laplacian semipositone equations

Boundary Value Problems20062006:87483

DOI: 10.1155/BVP/2006/87483

Accepted: 10 November 2005

Published: 23 February 2006

## 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.

## Authors’ Affiliations

(1)
Department of Mathematics, School of Science, The Behrend College
(2)
Department of Mathematics and Statistics, Mississippi State University

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