Description

• Title:
  Existence of solutions for a Kirchhoff type fractional differential equations via minimal principle and Morse theory
• Creator:
  Nyamoradi, Nemat;
  Zhou, Yong
• Description:
  In this paper by using the minimal principle and Morse theory, we prove the existence of solutions to the following Kirchhoff type fractional differential equation: \begin{equation*} \begin{cases} M (\int_{\mathbb{R}} (|{}_{- \infty} D_t^\alpha u (t)|^2 + b (t) |u(t)|^2 )\, d t) \cdot ({}_tD_\infty^{\alpha} ({}_{- \infty} D_t^\alpha u (t) ) + b(t) u (t)) = f (t, u (t)), t \in \mathbb{R}, u \in H^\alpha (\mathbb{R}), \end{cases} \end{equation*} where $\alpha \in ({1}/{2},1)$, ${}_tD_\infty^{\alpha}$ and ${}_{- \infty} D_t^\alpha$ are the right and left inverse operators of the corresponding Liouville--Weyl fractional integrals of order $\alpha$ respectively, $H^\alpha$ is the classical fractional Sobolev Space, $u \in \mathbb{R}$, $b \colon \mathbb{R} \to \mathbb{R}$, $\inf\limits_{t \in \mathbb{R}} b (t) \ge 0$, $f \colon \mathbb{R}\times \mathbb{R} \to \mathbb{R}$ Caratheodory function and $M\colon \mathbb{R}^+ \to \mathbb{R}^+$ is a~function that satisfy some suitable conditions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 617 - 630;
  1230-3429
• Format:
  application/pdf
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.061/7234 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.061/7235
• Subject:
  Fractional differential equations;
  minimal principle;
  Morse theory;
  solutions;
  Critical point theory;
  34C37;
  35A15;
  35B38
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.061
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other