Isolated singularities for the exponential type semilinear elliptic equation in ℝ²

Dhanya, R.; Giacomoni, J.; Prashanth, S.

doi:10.1090/S0002-9939-09-09988-2

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 PDF

Proc. Amer. Math. Soc. 137 (2009), 4099-4107 Request permission

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.

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