Description

• Title:
  On exact multiplicity for a second order equation with radiation boundary conditions
• Creator:
  Amster, Pablo;
  Kuna, Mariel P.
• Description:
  A second order ordinary differential equation with a superlinear term $g(x,u)$ under radiation boundary conditions is studied. Using a shooting argument, all the results obtained in the previous work \cite{AKR3} for a Painlevé II equation are extended. It is proved that the uniqueness or multiplicity of solutions depend on the interaction between the mapping $\frac {\partial g}{\partial u}(\cdot,0)$ and the first eigenvalue of the associated linear operator. Furthermore, two open problems posed in \cite{AKR3} regarding, on the one hand, the existence of sign-changing solutions and, on the other hand, exact multiplicity are solved.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.07.13
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 1 (September 2019); 233 - 246;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.039/18009 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.039/18010
• Subject:
  Second order ODEs;
  radiation boundary conditions;
  multiple solutions;
  electro-diffusion models;
  Primary;
  34B15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.039
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other