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2005, 2005(Special): 587-596. doi: 10.3934/proc.2005.2005.587

Explicit necessary and sufficient conditions for the existence of a dead core solution of a p-laplacian steady-state reaction-diffusion problem

Shin-Yi Lee 1, , Shin-Hwa Wang 2, and  Chiou-Ping Ye 2,

1. 

Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, Republic of China
2. 

Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 300, China, China

Received  July 2004 Revised  April 2005 Published  September 2005

We establish explicit necessary and sufficient conditions for the existence of a dead core solution of a $p$-Laplacian steady-state reaction-diffusion problem. The gap is extremely small between the explicit necessary condition and the explicit sufficient condition for the existence of a dead core solution.
Keywords: Lipschitz condition., existence, p-Laplacian, Reaction-diffusion problem, dead core solution, uniqueness.
Mathematics Subject Classification: 35J65, 34B1.
Citation: Shin-Yi Lee, Shin-Hwa Wang, Chiou-Ping Ye. Explicit necessary and sufficient conditions for the existence of a dead core solution of a p-laplacian steady-state reaction-diffusion problem. Conference Publications, 2005, 2005 (Special) : 587-596. doi: 10.3934/proc.2005.2005.587
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