@Article{JPDE-30-4,
author = {Joseph, Iaia, A.},
title = {Existence and Nonexistence for Semilinear Equations on Exterior Domains},
journal = {Journal of Partial Differential Equations},
year = {2017},
volume = {30},
number = {4},
pages = {299--316},
abstract = {<p>In this paper we prove the existence of an infinite number of radial solutions of $\Delta u + K(r)f(u)= 0$ on the exterior of the ball of radius $R&gt;0$ centered at the origin in ${\mathbb R}^{N}$ where $f$ is odd with $f&lt;0$ on $(0, \beta) $, $f&gt;0$ on $(\beta, \delta),$&nbsp; $f\equiv 0$ for $u&gt; \delta$, and where the function $K(r)$ is assumed to be positive and $K(r)\to 0$ as $r \to \infty.$ The primitive $F(u)&nbsp; = \int_{0}^{u} f(s) \, {\rm d}s$ has a&nbsp; ``hilltop&#39;&#39; at $u=\delta$ which allows one to use the shooting method to prove the existence of solutions.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v30.n4.2},
url = {https://global-sci.com/article/88237/existence-and-nonexistence-for-semilinear-equations-on-exterior-domains}
}