Geodesic
Existence and multiplicity results for critical and subcritical $p$-fractional elliptic equations via Nehari manifold method
Novi Sad Journal of Mathematics, Tome 52 (2022) no. 2 Cet article a éte moissonné depuis la source Novi sad journal of mathematics website

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In this paper, we establish the multiplicity of nonnegative solutions to the following p-fractional Laplacian problem% \begin{equation*} \left\{ \begin{array}{l} \mathbf{(-}\Delta \mathbf{)}_{p}^{s}u=f(x,u)+\lambda g(x,u)\ \text{in }% \Omega \ ,u>0, \\ \\ u=0\text{ on}\ \mathbb{R}^{n}\setminus \Omega ,% \end{array}% \right. \end{equation*}% where $\Omega $ is a smooth bounded set in $\mathbb{R}^{n},n>ps$ with $s\in (0,1),\lambda $ is a positive parameter,$\ f,g$ are homogeneous positive functions of degrees $q$ and $r\ $respectively. Using fibering maps and the Nehari manifold, we obtain some results in subcritical and critical cases.
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DOI : 10.30755/NSJOM.11897
Classification : 35P30, 35J35, 35J60
Keywords: fractional operator, Nehari manifold, fibering method 
@article{10.30755/NSJOM.11897,
     author = {Kamel Akrout and Mounira Azouzi and Hasna Yousfi},
     title = {Existence and multiplicity results for critical and subcritical $p$-fractional elliptic equations via {Nehari} manifold method
},
     journal = {Novi Sad Journal of Mathematics},
     pages = {111 - 126},
     year = {2022},
     volume = {52},
     number = {2},
     doi = {10.30755/NSJOM.11897},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.11897/}
}
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%A Mounira Azouzi
%A Hasna Yousfi
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%J Novi Sad Journal of Mathematics
%D 2022
%P 111 - 126
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%U http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.11897/
%R 10.30755/NSJOM.11897
%F 10.30755/NSJOM.11897
Kamel Akrout; Mounira Azouzi; Hasna Yousfi. Existence and multiplicity results for critical and subcritical $p$-fractional elliptic equations via Nehari manifold method. Novi Sad Journal of Mathematics, Tome 52 (2022) no. 2. doi: 10.30755/NSJOM.11897

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