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1 results

  • Extremal Positive Solutions of Semilinear Schrödinger Equations

  • C. A. Swanson
  • Journal:
    Canadian Mathematical Bulletin / Volume 26 / Issue 2 / 01 June 1983
    Published online by Cambridge University Press:
    20 November 2018, pp. 171-178
    Print publication:
    01 June 1983
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  • Necessary and sufficient conditions are proved for the existence of maximal and minimal positive solutions of the semilinear differential equation Δu = -ƒ(x, u) in exterior domains of Euclidean n-space. The hypotheses are that ƒ(x, u) is nonnegative and Hölder continuous in both variables, and bounded above and below by ugi(| x |, u), i = 1, 2, respectively, where each gi(r, u) is monotone in u for each r > 0.