Description

• Title:
  Corrigendum and addendum to "Non-autonomous quasilinear elliptic equations and Ważewski's principle"
• Creator:
  Franca, Matteo
• Description:
  In this addendum we fill a gap in a proof and we correct some results appearing in \cite{F6}. In the original paper \cite{F6} we classified positive solutions for the following equation \begin{equation*} \Delta_{p}u+K(r) u^{\sigma-1}=0 \end{equation*} where $r=|x|$, $x \in \RR^n$, $n> p> 1$, $\sigma ={n p}/({n-p})$ and $K(r)$ is a function strictly positive and bounded. In fact \cite{F6} had two main purposes. First, to establish asymptotic conditions which are sufficient for the existence of ground states with fast decay and to classify regular and singular solutions: these results are correct but need some non-trivial further explanations. Second to establish some computable conditions on $K$ which are sufficient to obtain multiplicity of ground states with fast decay in a non-perturbation context. Also in this case the original argument contained a flaw: here we correct the assumptions of \cite{F6} by performing a new nontrivial construction. A third purpose of this addendum is to generalize results of \cite{F6} to a slightly more general equation \begin{equation*} \Delta_p u+ r^{\delta}K(r) u^{\sigma(\delta)-1}=0 \end{equation*} where $\delta> -p$, and $\sigma(\delta) ={p(n+\delta)}/({n-p})$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.09.05
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 56, No 1 (September 2020); 1 - 30;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.110/26454 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.110/26455
• Subject:
  $p$-laplace equations;
  invariant manifold;
  non-smooth systems;
  radial solutions;
  ground states;
  Fowler transformation;
  Ważewski's principle;
  Primary;
  35J92;
  37D10;
  Secondary;
  34C37;
  34C45
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.110
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other