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Existence results for classes of -Laplacian semipositone equations

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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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