Junping Shi, Miaoxin Yao
We study an elliptic boundary-value problem with singular nonlinearity via the method of monotone iteration scheme:
where is the Laplacian operator, is a bounded domain in , , may take the value 0 on , and is possibly singular near . We prove the existence and the uniqueness of positive solutions under a set of hypotheses that do not make neither monotonicity nor strict positivity assumption on which improvements of some previous results.
Submitted August 15, 2004. Published January 2, 2005.
Math Subject Classifications: 35J25, 35J60.
Key Words: Singular nonlineararity; elliptic equation; positive solution; monotonic iteration.
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| Junping Shi |
Department of Mathematics, College of William and Mary
Williamsburg, VA 23187, USA
Department of Mathematics, Harbin Normal University
Harbin, Heilongjiang, China
| Miaoxin Yao |
Department of Mathematics, Tianjin University
and Liu Hui Center for Applied Mathematics
Nankai University & Tianjin University
Tianjin, 300072, China
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