Existence of entire radial solutions to a class of quasilinear elliptic equations and systems
In this paper, by a monotone iterative method and the Arzèla-Ascoli theorem, we obtain the existence of entire positive radial solutions to the following quasilinear elliptic equations \[\operatorname{div}(\phi_1(|\nabla u|) \nabla u)+a_1(|x|) \phi_1(|\nabla u|) |\nabla u|=b_1(|x|)f(u), \qquad x\in...
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2016-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4782 |
| Summary: | In this paper, by a monotone iterative method and the Arzèla-Ascoli theorem, we obtain the existence of entire positive radial solutions to the following quasilinear elliptic equations
\[\operatorname{div}(\phi_1(|\nabla u|) \nabla u)+a_1(|x|) \phi_1(|\nabla u|)
|\nabla u|=b_1(|x|)f(u), \qquad x\in \mathbb R^N,\]
and systems
\begin{cases}
\operatorname{div}(\phi_1(|\nabla u|) \nabla u)+a_1(|x|) \phi_1(|\nabla u|)
|\nabla u| =b_1(|x|)f_1(u, v), &x\in \mathbb R^N, \\
\operatorname{div}(\phi_2(|\nabla v|) \nabla v)
+a_2(|x|)\phi_2(|\nabla v|) |\nabla v|=b_2(|x|)f_2(u, v), &x\in \mathbb R^N,
\end{cases}
under simple conditions on $f$, $f_i$, $a_i$ and $b_i$ ($i=1, 2$). |
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| ISSN: | 1417-3875 |