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Research Article
A singular nonlinear elliptic equation with natural growth in the gradient
Article first published online: 20 FEB 2008
DOI: 10.1002/mma.996
Copyright © 2008 John Wiley & Sons, Ltd.
Issue
1099-1476/asset/cover.gif?v=1&s=7f3c8599d848bbeeab682f114551621db8fd932e "Mathematical Methods in the Applied Sciences")
Mathematical Methods in the Applied Sciences
Volume 31, Issue 14, pages 1704–1721, 25 September 2008
Additional Information
How to Cite
Zhou, W.-S. (2008), A singular nonlinear elliptic equation with natural growth in the gradient. Math. Meth. Appl. Sci., 31: 1704–1721. doi: 10.1002/mma.996
Publication History
- Issue published online: 7 AUG 2008
- Article first published online: 20 FEB 2008
- Manuscript Received: 30 JUN 2007
Funded by
- Dalian Nationalities University
- NNSFC
- Abstract
- References
- Cited By
Keywords:
- nonlinear elliptic equation;
- singularity;
- existence;
- regularity;
- boundary blowup
Abstract
This paper is devoted to the existence and regularity of the homogenous Dirichlet boundary value problem for a singular nonlinear elliptic equation with natural growth in the gradient. By certain transformations, the problem can be transformed formally into either a Dirichlet problem or boundary blowup problems without gradient term, for which the corresponding existence results are also derived, which is a partial extension and supplement to the previous works. Copyright © 2008 John Wiley & Sons, Ltd.