Liouville's Theorem in the Radially Symmetric Case
Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 405-408

Voir la notice de l'article provenant de la source Cambridge University Press

We present a very short proof of Liouville's theorem for solutions to a non-uniformly elliptic radially symmetric equation. The proof uses the Ricatti equation satisfied by the Dirichlet to Neumann map.
DOI : 10.4153/CMB-2005-037-7
Mots-clés : 35B05, 34A30
Froese, Richard. Liouville's Theorem in the Radially Symmetric Case. Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 405-408. doi: 10.4153/CMB-2005-037-7
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[B] Barlow, M. T., On the Liouville property for divergence form operators. Canad. J. Math. 50(1998), 487–496. Google Scholar

[BCN] Berestycki, H., Caffarelli, L., and Nirenberg, L., Further qualitative properties for elliptic equations in unbounded domains. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25(1997), 69–94. Google Scholar

[GG] Ghoussoub, N. and Gui, C., On a conjecture of De Giorgi and some related problems. Math. Ann. 311(1998), 481–491. Google Scholar

[L] Losev, A. G., Some Liouville theorems on Riemannian manifolds of a special type. Izv. Vyssh. Uchebn. Zaved. Mat. (1991), 15–24; English Transl., Soviet Math. (Iz. VUZ) 35(1991), 15–23. Google Scholar

[LM] Losev, A. G. and Mazepa, E. A., Bounded solutions of the Schrödinger equation on Riemannian products. (Russian) Algebra i Analiz 13(2001), 84–110. translation in St. PetersburgMath. J. 13(2002), 57–73. Google Scholar

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