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Existence results for classes of -Laplacian semipositone equations

Boundary Value Problems volume 2006, Article number: 87483 (2006) Cite this article

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.

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Author information

Affiliations

  1. Department of Mathematics, School of Science, The Behrend College, Penn State Erie, Erie, PA, 16563, USA

    Shobha Oruganti

  2. Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS, 39762, USA

    R Shivaji

Authors
  1. Shobha Oruganti
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  2. R Shivaji
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Correspondence to R Shivaji.

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Oruganti, S., Shivaji, R. Existence results for classes of -Laplacian semipositone equations. Bound Value Probl 2006, 87483 (2006). https://doi.org/10.1155/BVP/2006/87483

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Keywords

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