Open AccessOn a nonlocal problem involving the fractional $ p(x,.) $-Laplacian satisfying Cerami condition
Author(s) -
Elhoussine Azroul,
Abdelmoujib Benkirane,
and Mohammed Shimi
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2020425
Subject(s) - mathematics , fractional laplacian , combinatorics , dirichlet boundary condition , class (philosophy) , graph , laplace operator , boundary value problem , pure mathematics , mathematical analysis , computer science , artificial intelligence
The present paper deals with the existence and multiplicity of solutions for a class of fractional \begin{document}$ p(x,.) $\end{document} -Laplacian problems with the nonlocal Dirichlet boundary data, where the nonlinearity is superlinear but does not satisfy the usual Ambrosetti-Rabinowitz condition. To overcome the difficulty that the Palais-Smale sequences of the Euler-Lagrange functional may be unbounded, we consider the Cerami sequences. The main results are established by means of mountain pass theorem and Fountain theorem with Cerami condition.