Azroul, Elhoussine; Benkirane, Abdelmoujib; Shimi, Mohammed On a nonlocal problem involving the fractional \(p(x,.)\)-Laplacian satisfying Cerami condition. (English) Zbl 1473.35621 Discrete Contin. Dyn. Syst., Ser. S 14, No. 10, 3479-3495 (2021). Summary: The present paper deals with the existence and multiplicity of solutions for a class of fractional \(p(x,.)\)-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. Cited in 2 Documents MSC: 35R11 Fractional partial differential equations 35A15 Variational methods applied to PDEs 35J25 Boundary value problems for second-order elliptic equations 35J92 Quasilinear elliptic equations with \(p\)-Laplacian 47G30 Pseudodifferential operators 35S15 Boundary value problems for PDEs with pseudodifferential operators Keywords:fractional \(p(x,.)\)-Laplacian operator; nonlocal problem; Cerami condition; mountain pass theorem; Fountain theorem PDFBibTeX XMLCite \textit{E. Azroul} et al., Discrete Contin. Dyn. Syst., Ser. S 14, No. 10, 3479--3495 (2021; Zbl 1473.35621) Full Text: DOI References: [1] A. Ambrosetti; P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14, 349-341 (1973) · Zbl 0273.49063 [2] E. Azroul, A. Benkirane, M. Shimi and M. Srati, On a class of fractional \(\begin{document}p(x)\end{document} \)-Kirchhoff type problems, Applicable Analysis, 2019 (2019). · Zbl 1458.35445 [3] E. Azroul; A. 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