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Multiplicity results for a critical and subcritical system involving fractional $p$-Laplacian operator via Nehari manifold method
by Zediri Sounia   Akrout Kamel   Ghanmi Abdeljabbar

Vol. 17 No. 3 (2022) P.355~P.376
 DOI: https://doi.org/10.21915/BIMAS.2022304 10.21915/BIMAS.2022304

ABSTRACT

In this paper, we study the existence of multiple solutions to some sub-critical and critical systems involving the fractional p-Laplacian operator. Our main tools are based on variational methods. Precisely, the Nehari manifold method combined with fibering map are used in the study of the sub-critical case. While in the critical one, we use the mountain pass theorem combined with Nehari manifold and Brezis-Lieb lemma.

KEYWORDS
Variational method, Nehari manifold, elliptic equation, multiple solutions

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35P30, 35J35, 35J60

MILESTONES