Description

• Title:
  A three solutions theorem for Pucci's extremal operator and its application
• Creator:
  Mallick, Mohan;
  Verma, Ram Baran
• Description:
  In this article we prove a three solution type theorem for the following boundary value problem: \begin{equation*} \label{abs} \begin{cases} -\mathcal{M}_{\lambda,\Lambda}^+(D^2u) =f(u)& \text{in }\Omega,\\ u =0& \text{on }\partial\Omega, \end{cases} \end{equation*} where $\Omega$ is a bounded smooth domain in $\mathbb{R}^N$ and $f\colon [0,\infty]\to[0,\infty]$ is a $C^{\alpha}$ function. This is motivated by the work of Amann \cite{aman} and Shivaji \cite{shivaji1987remark}, where a three solutions theorem has been established for the Laplace operator. Furthermore, using this result we show the existence of three positive solutions to above boundary value by explicitly constructing two ordered pairs of sub and supersolutions when $f$ has a sublinear growth and $f(0)=0.$
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2021.09.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 58, No 1 (September 2021); 161 - 179;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/35210/29666 ;https://apcz.umk.pl/TMNA/article/view/35210/29667
• Subject:
  Nonlinear elliptic equations;
  sub and supersolution;
  fixed point;
  multiple positive solutions;
  Primary;
  35J25;
  35J60;
  Secondary;
  35D40;
  35A01
• Identifier: https://apcz.umk.pl/TMNA/article/view/35210
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other