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

@inproceedings{Dhanya2009IsolatedSF,
title={Isolated singularities for the exponential type semilinear elliptic equation in \$\mathbb \{R\}^2\$},
author={Rajendran Dhanya and Jacques Giacomoni and S. Prashanth},
year={2009}
}
• Published 15 July 2009
• Mathematics
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.
4 Citations
Radial singular solutions for the N-Laplace equation with exponential nonlinearities
• Mathematics
Journal of Mathematical Analysis and Applications
• 2019
Global bifurcation and local multiplicity results for elliptic equations with singular nonlinearity of super exponential growth in $\mathbb{R}^2$
• Mathematics
• 2012
In this paper, we study the solutions to the following singular elliptic problem of exponential type growth posed in a bounded smooth domain Ω ⊂ R2 : −∆u = λ(u−δ + h(u)eu ) in Ω, (Pλ) { u > 0 in
Isolated singularities of polyharmonic operator in even dimension
• Mathematics
• 2015
We consider the equation in the sense of distribution in where and . Then it is known that solves , for some nonnegative constants and . In this paper, we study the existence of singular solutions to
Analytic global bifurcation and infinite turning points for very singular problems
• Mathematics
• 2015
Let $$\Omega$$Ω be a domain in $$\mathbb {R}^N, N\ge 2$$RN,N≥2, $$\lambda >0$$λ>0 a bifurcation parameter and $$f: \mathbb {R}\rightarrow \mathbb {R}$$f:R→R a “real analytic” type map such that

## References

SHOWING 1-10 OF 14 REFERENCES
Global Compactness Properties of Semilinear Elliptic Equations with Critical Exponential Growth
• Mathematics
• 2000
Abstract Sequences of positive solutions to semilinear elliptic equations of critical exponential growth in the plane either are precompact in the Sobolev H 1 -topology or concentrate at isolated
Nonlinear elliptic equations with critical growth related to the Trudinger inequality
• Mathematics
• 1996
where fl is a two-dimensional bounded domain and A > 0 is a parameter. We study the family of solutions of (E) satisfying the following condition (B): IlulluX) -+ 00 as A -+ O. (B) The existence of
Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
• Mathematics
• 1975
Abstract : Continuation and variational methods are developed to construct positive solutions for nonlinear elliptic eigenvalue problems. The class of equations studied contain in particular models
Bifurcation, perturbation of simple eigenvalues, itand linearized stability
• Mathematics
• 1973
Abstract : The eigenvalue of minimum modulus of the Frechet derivative of a nonlinear operator is estimated along a bifurcating curve of zeroes of the operator. This result is applied to the study of
Failure of Plais-Smale condition and blow-up analysis for the critical exponent problem inR2
• Mathematics
• 1997
AbstractLet Ω be a bounded smooth domain inR2. Letf:R→R be a smooth non-linearity behaving like exp{s2} ass→∞. LetF denote the primitive off. Consider the functionalJ:H01(Ω)→R given by J(u) =
PARTIAL DIFFERENTIAL EQUATIONS
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