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arXiv · 1111.2207

Entire large solutions for semilinear elliptic equations

Louis Dupaigne·Marius Ghergu·Olivier Goubet·Guillaume Warnault
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Abstract

We analyze the semilinear elliptic equation $\Delta u=\rho(x) f(u)$, $u>0$ in ${\mathbf R}^D$ $(D\ge3)$, with a particular emphasis put on the qualitative study of entire large solutions, that is, solutions $u$ such that $\lim_{|x|\rightarrow +\infty}u(x)=+\infty$. Assuming that $f$ satisfies the Keller-Osserman growth assumption and that $\rho$ decays at infinity in a suitable sense, we prove the existence of entire large solutions. We then discuss the more delicate questions of asymptotic behavior at infinity, uniqueness and symmetry of solutions.

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Louis Dupaigne, Marius Ghergu, Olivier Goubet, Guillaume Warnault. 2011-11-09. Entire large solutions for semilinear elliptic equations. https://doi.org/10.1016/j.jde.2012.05.024

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