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arXiv · 1807.05918

Radial singular solutions for the N-Laplace Equation with exponential nonlinearities

M. Ghergu·J. Giacomoni·S. Prashanth
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Abstract

In this paper, we consider radial distributional solutions of the quasilinear equation $-Δ_N u=f(u)$ in the punctured open ball $ B_R\backslash\{0\}\subset \RR^N$, $N \geq 2$. We obtain sharp conditions on the nonlinearity $f$ for extending such solutions to the whole domain $B_R$ by preserving the regularity. For a certain class of noninearity $f$ we obtain the existence of singular solutions and deduce upper and lower estimates on the growth rate near the singularity.

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M. Ghergu, J. Giacomoni, S. Prashanth. 2018-07-16. Radial singular solutions for the N-Laplace Equation with exponential nonlinearities. https://arxiv.org/abs/1807.05918

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