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Large Solutions of a Class of Semilinear Elliptic Equations

Author: XuZuo
Tutor: ZhouFeng
School: East China Normal University
Course: Applied Mathematics
Keywords: Semilinear elliptic equations Large solution Existence Asymptotic behavior Uniqueness
CLC: O175.25
Type: Master's thesis
Year: 2006
Downloads: 57
Quote: 0
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Abstract


In this paper,we consider the semilinear elliptic equation:The exitence,uniquness and asymptotic behavior of large solutions are considered.This equation has always been the hotspot in Partial Differential Equation.We notice that the solution blow-up on the boundary,so it is very important to study the asymptotic behavior of large solution.Our framework includes two cases:Ω is a smooth bounded domain in R~N;Ω= R~N .We compare the condition of p and f and summarize the method and tools which are frequently used.We also expound some important proofs in detail.In particular,we discussed that when p(x) = 1,the asymptotic behavior of large solutions is in concern with the mean curvature.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Elliptic equations
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