Description

• Tytuł:
  On extreme values of Nehari manifold method via nonlinear Rayleigh's quotient
• Twórca:
  Il'yasov, Yavdat
• Opis:
  We study applicability conditions of the Nehari manifold method to the equation of the form $D_u T(u)-\lambda D_u F(u)=0$ in a Banach space $W$, where $\lambda$ is a real parameter. Our study is based on the development of the Rayleigh quotient theory for nonlinear problems. It turns out that the extreme values of parameter $\lambda$ which define intervals of applicability of the Nehari manifold method can be found through the critical values of the corresponding nonlinear generalized Rayleigh quotient. In the main part of this paper, we provide general results on this relationship. Theoretical results are illustrated by considering several examples of nonlinear boundary value problems. Furthermore, we demonstrate that the introduced tool of nonlinear generalized Rayleigh quotient can also be applied to prove new results on the existence of multiple solutions for nonlinear elliptic equations.
• Dostępność obiektu:
  free access
• Prawa:
  Prawa autorskie (c) 2017 Topological Methods in Nonlinear Analysis
• Data:
  2017.03.04
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  English
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 49, No 2 (June 2017); 683 - 714;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.005/11350 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.005/11351
• Temat i słowa kluczowe:
  Nehari manifold;
  Rayleigh's quotient;
  nonlinear system of equations;
  Primary;
  35J50;
  35J55;
  Secondary;
  35J60
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.005
• Dostawca danych:
  Akademicka Platforma Czasopism
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