Year: 2017
Author: Joseph A. Iaia
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 4 : pp. 299–316
Abstract
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 $R>0$ centered at the origin in ${\mathbb R}^{N}$ where $f$ is odd with $f<0$ on $(0, \beta) $, $f>0$ on $(\beta, \delta),$ $f\equiv 0$ for $u> \delta$, and where the function $K(r)$ is assumed to be positive and $K(r)\to 0$ as $r \to \infty.$ The primitive $F(u) = \int_{0}^{u} f(s) \, {\rm d}s$ has a ``hilltop'' at $u=\delta$ which allows one to use the shooting method to prove the existence of solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v30.n4.2
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 4 : pp. 299–316
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Semilinear
Author Details
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