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Title: Classification of positive solutions of $p$-Laplace equation with a growth term (English)
Author: Franca, Matteo
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 40
Issue: 4
Year: 2004
Pages: 415-434
Summary lang: English
Category: math
Summary: We give a structure result for the positive radial solutions of the following equation: \[ \Delta _{p}u+K(r) u|u|^{q-1}=0 \] with some monotonicity assumptions on the positive function $K(r)$. Here $r=|x|$, $x \in {\mathbb R}^n$; we consider the case when $n>p>1$, and $q >p_* =\frac{n(p-1)}{n-p}$. We continue the discussion started by Kawano et al. in [KYY], refining the estimates on the asymptotic behavior of Ground States with slow decay and we state the existence of S.G.S., giving also for them estimates on the asymptotic behavior, both as $r \rightarrow 0$ and as $r \rightarrow \infty $. We make use of a Emden-Fowler transform which allow us to give a geometrical interpretation to the functions used in [KYY] and related to the Pohozaev identity. Moreover we manage to use techniques taken from dynamical systems theory, in particular the ones developed in [JPY2] for the problems obtained by substituting the ordinary Laplacian $\Delta $ for the $p$-Laplacian $\Delta _{p}$ in the preceding equations. (English)
Keyword: $p$-Laplace equations
Keyword: radial solution
Keyword: regular/singular ground state
Keyword: Fowler inversion
Keyword: invariant manifold
MSC: 35B05
MSC: 35H30
MSC: 35J60
MSC: 37D10
idZBL: Zbl 1110.37018
idMR: MR2129963
Date available: 2008-06-06T22:44:45Z
Last updated: 2012-05-10
Stable URL:
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