L stability of an exponentially decreasing solution of the problem Δu+f(x, u)=0 inR n

  • Hiroshi Matano


We consider the Cauchy problemu t=δu+f(x, u), x∈Rn, t>0, and prove that if there exist a strict supersolution\(\bar w\left( x \right)\) and a strict subsolutionw(x) with\(\bar w > w\) then there exists at least one stable equilibrium solution between\(\bar w\) andw provided thatf satifies certain conditions. The stability is with respect to theL norm. Unlike the case where the spatial domain is bounded, some difficulties occur near |x|=∞ in the present problem. The major part of this paper is devoted to dealing with such difficulties.

Key words

semilinear elliptic equation inRn super- and subsolutions stability semilinear diffusion equation 


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Copyright information

© JJAM Publishing Committee 1985

Authors and Affiliations

  • Hiroshi Matano
    • 1
  1. 1.Department of MathematicsHiroshima UniversityHiroshimaJapan

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