Description

• Title:
  Existence of sign-changing solutions for one-dimensional $p$-Laplacian problems with a singular indefinite weight
• Creator:
  Lee, Yong-Hoon;
  Sim, Inbo
• Description:
  In this paper, we establish a sequence $\{\nu_k^\infty\}$ of eigenvalues for the following eigenvalue problem $$ \cases \varphi_p (u'(t))' + \nu h(t) \varphi_p(u(t)) = 0 &\text{for } t \in (0,1), \\ u(0) = 0=u(1), \endcases $$ where $\varphi_p(x)=|x|^{p-2}x$, $ 1< p< 2$, $\nu$ a real parameter. In particular, $h \in C((0,1),(0,\infty))$ is singular at the boundaries which may not be of $L^1(0,1)$. Employing global bifurcation theory and approximation technique, we prove several existence results of sign-changing solutions for problems of the form $$ \cases \varphi_p (u'(t))' + \lambda h(t) f (u(t)) = 0 &\text{for } t \in (0,1), \\ u(0) = 0= u(1), \endcases \tag{QP$_\lambda$} $$ when $f \in C({\mathbb{R}}, {\mathbb{R}})$ and $uf(u) > 0$, for all $u \neq 0$ and is odd with various combinations of growth conditions at $0$ and $\infty$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 36, No 1 (September 2010); 61 - 90;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.028/8451
• Subject:
  Singular one-dimensional p-Laplacian;
  global bifurcation;
  existence;
  Lusternik-Schnirelmann theory;
  Hardy inequality;
  47J10;
  34B15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.028
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other