Extremal Positive Solutions of Semilinear Schrödinger Equations
- 1 June 1983
- journal article
- Published by Canadian Mathematical Society in Canadian Mathematical Bulletin
- Vol. 26 (2) , 171-178
- https://doi.org/10.4153/cmb-1983-028-3
Abstract
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
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