The Nehari manifold for a boundary value problem involving Riemann–Liouville fractional derivative

Autor: Kamel Saoudi, Praveen Agarwal, Poom Kumam, Abdeljabbar Ghanmi, Phatiphat Thounthong
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Zdroj: Advances in Difference Equations, Vol 2018, Iss 1, Pp 1-18 (2018)
Druh dokumentu: article
ISSN: 1687-1847
DOI: 10.1186/s13662-018-1722-8
Popis: Abstract We aim to investigate the following nonlinear boundary value problems of fractional differential equations: (Pλ){−tD1α(|0Dtα(u(t))|p−20Dtαu(t))=f(t,u(t))+λg(t)|u(t)|q−2u(t)(t∈(0,1)),u(0)=u(1)=0, $$\begin{aligned} (\mathrm{P}_{\lambda}) \left \{ \textstyle\begin{array}{l} -_{t}D_{1}^{\alpha} ( \vert {}_{0}D_{t}^{\alpha}(u(t)) \vert ^{p-2} {}_{0}D_{t}^{\alpha}u(t) ) \\ \quad=f(t,u(t))+\lambda g(t) \vert u(t) \vert ^{q-2}u(t)\quad (t\in(0,1)),\\ u(0)=u(1)=0, \end{array}\displaystyle \right . \end{aligned}$$ where λ is a positive parameter, 2
Databáze: Directory of Open Access Journals
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