Loitering at the hilltop on exterior domains
In this paper we prove the existence of an infinite number of radial solutions of $\Delta u + f(u)= 0$ on the exterior of the ball of radius $R>0$ centered at the origin and $f$ is odd with $f<0$ on $(0, \beta) $, $f>0$ on $(\beta, \delta),$ and $f\equiv 0$ for $u> \delta$. The primitive...
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| Format: | Article |
| Language: | English |
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University of Szeged
2015-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4163 |
| Summary: | In this paper we prove the existence of an infinite number of radial solutions of $\Delta u + f(u)= 0$ on the exterior of the ball of radius $R>0$ centered at the origin and $f$ is odd with $f<0$ on $(0, \beta) $, $f>0$ on $(\beta, \delta),$ and $f\equiv 0$ for $u> \delta$. The primitive $F(u) = \int_{0}^{u} f(t) \, dt$ has a "hilltop" at $u=\delta$ which allows one to use the shooting method and ODE techniques to prove the existence of solutions. |
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| ISSN: | 1417-3875 |