Description

• Title:
  Singular reaction diffusion equations where a parameter influences the reaction term and the boundary conditions
• Creator:
  Fonseka, Nalin;
  Muthunayake, Amila;
  Shivaji, Ratnasingham;
  Son, Byungjae
• Description:
  We analyse positive solutions to the steady state reaction diffusion equation: \begin{equation*} \label{1.11} \begin{cases} -u''=\lambda h(t) f(u) \quad \text{in } (0,1), \\ -du'(0)+\mu(\lambda) u(0)=0,\\ u'(1)+\mu(\lambda) u(1)=0, \end{cases} \end{equation*} where $\lambda> 0$ is a parameter, $d\geq 0$ is a constant, $f \in C^2([0,\infty),\mathbb{R}) $ is an increasing function which is sublinear at infinity $\Big (\lim\limits_{s \rightarrow \infty}{f(s)}/{s}=0\Big)$, $h \in C^1((0,1],(0,\infty))$ is a nonincreasing function with $h_1:=h(1)> 0$ and there exist constants $d_0> 0$, $\alpha \in [0,1)$ such that $h(t)\leq {d_0}/{t^\alpha}$ for all $t \in (0,1]$, and $\mu \in C([0,\infty),[0,\infty))$ is an increasing function such that $\mu(0)\geq 0$. We consider three cases of $f$, namely, $f(0)=0$, $f(0)> 0$ and $f(0)< 0$. We will discuss existence and multiplicity results via the method of sub-supersolutions. Further, we will establish uniqueness results for $\lambda\approx 0$ and $\lambda\gg 1$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.02.08
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 1 (March 2021); 221 - 242;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.022/28137 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.022/28138
• Subject:
  Boundary value problems;
  singular problems;
  positive solutions;
  Primary;
  34B08;
  34B15;
  Secondary;
  34B16;
  34B18
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.022
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other