# Existence results for classes of -Laplacian semipositone equations

- Shobha Oruganti
^{1}and - R Shivaji
^{2}Email author

**2006**:87483

**DOI: **10.1155/BVP/2006/87483

© S. Oruganti and R. Shivaji 2006

**Received: **22 September 2005

**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

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## Copyright

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