Geodesic
Asymptotic Theory of Singular Semilinear Elliptic Equations
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 223-232

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DOI

Necessary and sufficient conditions are found for the existence of two positive solutions of the semilinear elliptic equation Δu + q(|x|)u = f(x, u) in an exterior domain Ω⊂Rn, n ≥ 1, where q, f are real-valued and locally Hölder continuous, and f(x, u) is nonincreasing in u for each fixed x∈Ω. An example is the singular stationary Klein-Gordon equation Δu — k 2 u = p(x)u -λ where k and λ are positive constants. In this case NASC are given for the existence of two positive solutions u i (x) in some exterior subdomain of Ω such that both |x|m exp[(-l)i-1 k|x|]u i (x) are bounded and bounded away from zero in this subdomain, m = (n —1)/2, i = 1, 2.
DOI : 10.4153/CMB-1984-032-1
Mots-clés : 35B05, 35J60, 34C11, 34EXX 
Kusano, Takaŝi; Swanson, Charles A. Asymptotic Theory of Singular Semilinear Elliptic Equations. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 223-232. doi: 10.4153/CMB-1984-032-1
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     author = {Kusano, Taka\^{s}i and Swanson, Charles A.},
     title = {Asymptotic {Theory} of {Singular} {Semilinear} {Elliptic} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {223--232},
     year = {1984},
     volume = {27},
     number = {2},
     doi = {10.4153/CMB-1984-032-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-032-1/}
}
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