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 |
| _version_ | 1797830607552643072 |
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| author | Joseph Iaia |
| author_facet | Joseph Iaia |
| author_sort | Joseph Iaia |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T13:38:47Z |
| format | Article |
| id | doaj.art-d4262e6406674bf098484d67df5ff359 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:47Z |
| publishDate | 2015-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-d4262e6406674bf098484d67df5ff3592023-05-09T07:53:05ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752015-11-0120158211110.14232/ejqtde.2015.1.824163Loitering at the hilltop on exterior domainsJoseph Iaia0University of North Texas, TX, U.S.A.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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4163radialhilltopsemilinear |
| spellingShingle | Joseph Iaia Loitering at the hilltop on exterior domains Electronic Journal of Qualitative Theory of Differential Equations radial hilltop semilinear |
| title | Loitering at the hilltop on exterior domains |
| title_full | Loitering at the hilltop on exterior domains |
| title_fullStr | Loitering at the hilltop on exterior domains |
| title_full_unstemmed | Loitering at the hilltop on exterior domains |
| title_short | Loitering at the hilltop on exterior domains |
| title_sort | loitering at the hilltop on exterior domains |
| topic | radial hilltop semilinear |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4163 |
| work_keys_str_mv | AT josephiaia loiteringatthehilltoponexteriordomains |