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Existence, uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations

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Abstract

We study positive solutions of the Dirichlet problem: Δu(x)+f(u(x))=0,x∈D n,u(x)=0,x∈∂D n, whereD n is ann-ball. We find necessary and sufficient conditions for solutions to be nondegenerate. We also give some new existence and uniqueness theorems.

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Authors and Affiliations

  1. Department of Mathematics, The University of Michigan, 48109-1003, Ann Arbor, MI, USA

    Joel A. Smoller & Arthur G. Wasserman

Authors
  1. Joel A. Smoller
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  2. Arthur G. Wasserman
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Communicated by L. Nirenberg

Research supported in part by NSF Contract Number MCS 80-02337

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Smoller, J.A., Wasserman, A.G. Existence, uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations. Commun.Math. Phys. 95, 129–159 (1984). https://doi.org/10.1007/BF01468138

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  • DOI: https://doi.org/10.1007/BF01468138

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