Isolated singularities for the exponential type semilinear elliptic equation in $\mathbb {R}^2$
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- by R. Dhanya, J. Giacomoni and S. Prashanth
- Proc. Amer. Math. Soc. 137 (2009), 4099-4107
- DOI: https://doi.org/10.1090/S0002-9939-09-09988-2
- Published electronically: July 15, 2009
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Abstract:
In this article we study positive solutions of the equation $-\Delta u= f(u)$ in a punctured domain $\Omega ’=\Omega \setminus \{0\}$ in $\mathbb {R}^2$ and show sharp conditions on the nonlinearity $f(t)$ that enables us to extend such a solution to the whole domain $\Omega$ and also preserve its regularity. We also show, using the framework of bifurcation theory, the existence of at least two solutions for certain classes of exponential type nonlinearities.References
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Bibliographic Information
- R. Dhanya
- Affiliation: Tata Institute of Fundamental Research, Center for Applicable Mathematics, P.B. No. 6503, Sharadanagar, Chikkabommasandra, Bangalore 560065, India
- Email: dhanya@math.tifrbng.res.in
- J. Giacomoni
- Affiliation: Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de l’Adour, B.P. 576, 64012 Pau cedex, France
- MR Author ID: 641792
- Email: jgiacomo@univ-pau.fr
- S. Prashanth
- Affiliation: Tata Institute of Fundamental Research, Center for Applicable Mathematics, P.B. No. 6503, Sharadanagar, Chikkabommasandra, Bangalore 560065, India
- Email: pras@math.tifrbng.res.in
- Received by editor(s): September 30, 2008
- Published electronically: July 15, 2009
- Communicated by: Matthew J. Gursky
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 4099-4107
- MSC (2000): Primary 35B32, 35B65, 35J25, 35J60
- DOI: https://doi.org/10.1090/S0002-9939-09-09988-2
- MathSciNet review: 2538571