ON THE STABILITY OF THE POSITIVE RADIAL STEADY STATES FOR A SEMILINEAR CAUCHY PROBLEM INVOLVING CRITICAL EXPONENTS

Deng  Yinbin; Yang Fen

doi:10.1016/S0252-9602(08)60036-3

Acta mathematica scientia, Series B >

2008 , Vol. 28 >Issue 2: 348 - 354

DOI: https://doi.org/10.1016/S0252-9602(08)60036-3

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ON THE STABILITY OF THE POSITIVE RADIAL STEADY STATES FOR A SEMILINEAR CAUCHY PROBLEM INVOLVING CRITICAL EXPONENTS

Deng Yinbin ,
Yang Fen

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Department of Mathematics, Huazhong Normal University, Wuhan 430079, China

Received date: 2005-10-18

Revised date: 2006-08-21

Online published: 2008-04-20

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Abstract

This article is contributed to the Cauchy problem
$$ \left\{\begin{array}{ll} \D
\frac{\partial u}{\partial t}=
\Delta u+K( |x|)u^p \ \ \mbox{in} \ R^n \times(0,T),\\
u(x,0)=\varphi(x) \ \ \mbox{in} \ R^n ;
\end{array}
\right. $$
with initial function $\varphi \not \equiv 0$. The stability of positive radial steady state, which are positive solutions of △u+K( | x|)u^p=0, is obtained when p is critical for general K(|x|).

Key words： Stability; Cauchy problem; asymptotic stability

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Deng Yinbin , Yang Fen . ON THE STABILITY OF THE POSITIVE RADIAL STEADY STATES FOR A SEMILINEAR CAUCHY PROBLEM INVOLVING CRITICAL EXPONENTS[J]. Acta mathematica scientia, Series B, 2008 , 28(2) : 348 -354 . DOI: 10.1016/S0252-9602(08)60036-3

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