Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Isolated singularities for the exponential type semilinear elliptic equation in $\mathbb{R}^2$

Author(s): R. Dhanya; J. Giacomoni; S. Prashanth
Journal: Proc. Amer. Math. Soc. 137 (2009), 4099-4107.
MSC (2000): Primary 35B32, 35B65, 35J25, 35J60
Posted: July 15, 2009
MathSciNet review: 2538571
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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 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.

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