Description

• Title:
  Infinitely many solutions of superlinear fourth order boundary value problems
• Creator:
  Rynne, Bryan P.
• Description:
  We consider the boundary value problem \begin{gather*} u^{(4)}(x) =g(u(x)) + p(x,u^{(0)}(x),\dots,u^{(3)}(x)) , \quad x \in (0,1), \\ u(0) =u(1) =u^{(b)}(0) =u^{(b)}(1) =0, \end{gather*} where: \begin{itemize} \item[(i)] $g \colon \mathbb R \to \mathbb R$ is continuous and satisfies $\lim_{|\xi| \to \infty} g(\xi)/\xi =\infty$ ($g$ is < i> superlinear< /i> as $|\xi| \to \infty$), \item[(ii)] $p \colon [0,1] \times \mathbb R^4 \to \mathbb R$ is continuous and satisfies $$ |p(x,\xi_0,\xi_1,\xi_2,\xi_3)| \le C + \frac{1}{4} |\xi_0| , \quad x \in [0,1],\ (\xi_0,\xi_1,\xi_2,\xi_3) \in \mathbb R^4, $$ for some $C&gt; 0$, \item[(iii)] either $b=1$ or $b=2$. \end{itemize} We obtain solutions having specified nodal properties. In particular, the problem has infinitely many solutions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2002.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 19, No 2 (June 2002); 303 - 312;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.016/9651
• Subject:
  Fourth order Sturm-Liouville problem;
  superlinear problem;
  34B15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.016
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other