Description

• Title:
  Positive solutions for a $2n$th-order $p$-Laplacian boundary value problem involving all even derivatives
• Creator:
  Xu, Jiafa;
  Wei, Zhongli;
  Ding, Youzheng
• Description:
  In this paper, we investigate the existence and multiplicity of positive solutions for the following $2n$th-order $p$-Laplacian boundary value problem $$ \cases -(((-1)^{n-1}x^{(2n-1)})^{p-1})'\\ =f(t,x,-x^{\prime\prime},\ldots,(-1)^{n-1}x^{(2n-2)}) &\text{for } t\in [0,1], \\ x^{(2i)}(0)=x^{(2i+1)}(1)=0 & \text{for } i=0,\ldots,n-1, \endcases $$ where $n\ge 1$ and $f\in C([0,1]\times \mathbb{R}_+^{n}, \mathbb{R}_+)(\mathbb{R}_+:=[0,\infty))$ depends on $x$ and all derivatives of even orders. Based on a priori estimates achieved by utilizing properties of concave functions and Jensen's integral inequalities, we use fixed point index theory to establish our main results. Moreover, our nonlinearity $f$ is allowed to grow superlinearly and sublinearly.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2012.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 39, No 1 (March 2012); 23 - 36;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.002/8352
• Subject:
  p-Laplacian equation;
  Jensen's inequality;
  positive solution;
  fixed point index;
  cone;
  34B18;
  47H07;
  47H11;
  45M20;
  26D15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2012.002
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other