Geodesic
Extremal Positive Solutions of Semilinear Schrödinger Equations
Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 171-178

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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.
DOI : 10.4153/CMB-1983-028-3
Mots-clés : Primary: 35B05, Secondary: 35J60 
Swanson, C. A. Extremal Positive Solutions of Semilinear Schrödinger Equations. Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 171-178. doi: 10.4153/CMB-1983-028-3
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     author = {Swanson, C. A.},
     title = {Extremal {Positive} {Solutions} of {Semilinear} {Schr\"odinger} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {171--178},
     year = {1983},
     volume = {26},
     number = {2},
     doi = {10.4153/CMB-1983-028-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-028-3/}
}
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