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

  title={Isolated singularities for the exponential type semilinear elliptic equation in \$\mathbb \{R\}^2\$},
  author={Rajendran Dhanya and Jacques Giacomoni and S. Prashanth},
In this article we study positive solutions of the equation -Δu = f (u) in a punctured domain Ω' = Ω \ {0} in ℝ 2 and show sharp conditions on the nonlinearity f(t) that enables us to extend such a solution to the whole domain Ω 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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Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear first-order PDE Other ways to represent solutions Part II: Theory for linear