| Title:
|
Existence and multiplicity of solutions for a fractional $p$-Laplacian problem of Kirchhoff type via Krasnoselskii's genus (English) |
| Author:
|
Benhamida, Ghania |
| Author:
|
Moussaoui, Toufik |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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143 |
| Issue:
|
2 |
| Year:
|
2018 |
| Pages:
|
189-200 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We use the genus theory to prove the existence and multiplicity of solutions for the fractional $p$-Kirchhoff problem $$ \begin {cases} \displaystyle -\biggl [M \biggl (\int _{Q}\dfrac {\vert u(x)-u(y)\vert ^{p}}{\vert x-y \vert ^{N+ps}} {\rm d}x {\rm d}y\biggr )\biggr ]^{p-1} (-\Delta )_{p}^{s}u=\lambda h(x,u) \quad \text {in}\ \Omega , \\ u=0 \quad \text {on}\ \mathbb {R}^N \setminus \Omega , \end {cases} $$ where $\Omega $ is an open bounded smooth domain of $\mathbb {R}^N$, $p>1$, $N>ps$ with $s\in (0,1)$ fixed, $Q = \mathbb {R}^{2N}\setminus (C\Omega \times C\Omega )$, $\lambda > 0$ is a numerical parameter, $M$ and $h$ are continuous functions. (English) |
| Keyword:
|
existence results |
| Keyword:
|
genus theory |
| Keyword:
|
fractional $p$-Kirchhoff problem |
| MSC:
|
34A08 |
| MSC:
|
35A15 |
| MSC:
|
35B38 |
| idZBL:
|
Zbl 06890414 |
| idMR:
|
MR3831486 |
| DOI:
|
10.21136/MB.2017.0010-17 |
| . |
| Date available:
|
2018-06-11T11:02:43Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147244 |
| . |
| Reference:
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