Description

• Title:
  A Fredholm alternative for elliptic equations with interior and boundary nonlinear reactions
• Creator:
  Maroncelli, Daniel;
  Rivas, Mauricio A.
• Description:
  In this paper we study the existence of solutions to the following generalized nonlinear two-parameter problem \begin{equation*} a(u, v) = \lambda b(u, v) + \mu m(u, v) + \varepsilon F(u, v), \end{equation*} for a triple $(a, b, m)$ of continuous, symmetric bilinear forms on a real separable Hilbert space $V$ and nonlinear form $F$. This problem is a natural abstraction of nonlinear problems that occur for a large class of differential operators, various elliptic pde's with nonlinearities in either the differential equation and/or the boundary conditions being a special subclass. First, a Fredholm alternative for the associated linear two-parameter eigenvalue problem is developed, and then this is used to construct a nonlinear version of the Fredholm alternative. Lastly, the Steklov-Robin Fredholm equation is used to exemplify the abstract results.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2023 Daniel Maroncelli, Mauricio A. Rivas;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2023.09.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 62, No 1 (September 2023); 135 - 157;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/46307/36551 ;https://apcz.umk.pl/TMNA/article/view/46307/36552
• Temat i słowa kluczowe:
  Two-parameter Fredholm alternative;
  eigencurves;
  Robin-Steklov problems;
  nonlinear elliptic problems;
  nonlinear boundary conditions;
  35J60, 35J65
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/46307
• Dostawca danych:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other