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Extremal Positive Solutions of Semilinear Schrödinger Equations

Published online by Cambridge University Press:  20 November 2018

C. A. Swanson
C. A. Swanson*
Affiliation:
University of British ColumbiaVancouver, CanadaV6T 1Y4
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Abstract

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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.

Keywords

Primary: 35B05Secondary: 35J60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 171 - 178
Copyright
Copyright © Canadian Mathematical Society 1983

References

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