On a nonlocal problem involving the fractional $ p(x,.) $-Laplacian satisfying Cerami condition

Abstract

<p style='text-indent:20px;'>The present paper deals with the existence and multiplicity of solutions for a class of fractional <inline-formula><tex-math id="M2">\begin{document}$ p(x,.) $\end{document}</tex-math></inline-formula>-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.</p>