Abstract
The method of shooting is used to establish existence of positive radially symmetric solutions to nonlinear elliptic equations of the form Δu+f(r, u)=0 on annular regionsa<r=|x|<b inR N, satisfying Dirichlet or Neumann conditions on the boundary. This extends recent work done by Bandle, Coffman and Marcus. A result concerning uniqueness of such solutions is also extended.
Zusammenfassung
Mit Hilfe eines Schiessverfahrens wird die Existenz von Lösungen nichtlinearer Probleme der Form Δu+f(r, u)=0 in ringförmigen Gebieten nachgewiesen, die verschiedenen Randbedingungen genügen. Es wird auch ihre Eindeutigkeit untersucht. Diese Arbeit verallgemeinert gewisse Ergebnisse von Bandle, Coffman und Marcus.
Résumé
On utilise une méthode de tir pour établir l'existence de solutions de problèmes non linéaires du type Δu+f(r, u)=0 dans des anneaux, vérifiant différentes conditions aux limites. Ensuite on discute l'unicité de ces solutions. Ce travail généralise certains résultats de Bandle, Coffman et Marcus.
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References
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This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contract W-31-109-Eng-38. The author also wants to thank the Mathematics Institute, University of Basel, for supporting a visit in Oct., 1987 during which the project was initiated.
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Bandle, C., Kwong, M.K. Semilinear elliptic problems in annular domains. Z. angew. Math. Phys. 40, 245–257 (1989). https://doi.org/10.1007/BF00945001
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DOI: https://doi.org/10.1007/BF00945001