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TWO-SIDED ESTIMATES FOR POSITIVE SOLUTIONS OF SUPERLINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS
Published online by Cambridge University Press: 30 August 2018
Abstract
We give two-sided estimates for positive solutions of the superlinear elliptic problem $-\unicode[STIX]{x1D6E5}u=a(x)|u|^{p-1}u$ with zero Dirichlet boundary condition in a bounded Lipschitz domain. Our result improves the well-known a priori$L^{\infty }$-estimate and provides information about the boundary decay rate of solutions.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 465 - 473
- Copyright
- © 2018 Australian Mathematical Publishing Association Inc.
Footnotes
This work was supported in part by JSPS KAKENHI Grant Number JP18K03333.
References
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