Existence and multiplicity of solutions for a fractional $p$-Laplacian problem of Kirchhoff type via Krasnoselskii's genus

We use the genus theory to prove the existence and multiplicity of solutions for the fractional $p$-Kirchhoff problem \begin{cases} \displaystyle-\biggl[M \biggl(\int_Q\dfrac{\vert u(x)-u(y)\vert^p}{\vert x-y \vert^{N+ps}} {\rm d}x {\rm d}y\biggr)\biggr]^{p-1} (-\Delta)_p^su=\lambda h(x,u) \quad\...

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Bibliographic Details
Main Authors: Ghania Benhamida, Toufik Moussaoui
Format: Article
Language:English
Published: Institute of Mathematics of the Czech Academy of Science 2018-07-01
Series:Mathematica Bohemica
Subjects:
Online Access:http://mb.math.cas.cz/full/143/2/mb143_2_6.pdf