Geodesic
Asymptotic Properties of Semilinear Equations
Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 34-46

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We study the asymptotic properties of positive solutions to the semilinear equation — Δu = f(x, u). Existence and asymptotic estimates are obtained for solutions in exterior domains, as well as entire solutions, for n ≧ 2. The study uses integral operator equations in Rn , and convergence theorems for solutions of Poisson's equation in bounded domains. A consequence of the method is that more precise estimates can be obtained for the growth of solutions at infinity, than have been obtained by other methods. As a special case the results are applied to the generalized Emden-Fowler equation — Δu = p(x)u γ , for γ > 0
DOI : 10.4153/CMB-1989-006-3
Mots-clés : 34C10, 34C11, 34D10 
Edelson, Allan L. Asymptotic Properties of Semilinear Equations. Canadian mathematical bulletin, Tome 32 (1989) no. 1, pp. 34-46. doi: 10.4153/CMB-1989-006-3
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     author = {Edelson, Allan L.},
     title = {Asymptotic {Properties} of {Semilinear} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {34--46},
     year = {1989},
     volume = {32},
     number = {1},
     doi = {10.4153/CMB-1989-006-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-006-3/}
}
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