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Existence results for classes of -Laplacian semipositone equations
Boundary Value Problems volume 2006, Article number: 87483 (2006)
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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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
- Differential Equation
- Partial Differential Equation
- Ordinary Differential Equation
- Positive Constant
- Functional Equation