Critical concave convex Ambrosetti-Prodi type problem for fractional $p$-Laplacian

In this paper we consider a class of critical concave convex Ambrosetti-Prodi type problems for the fractional $p$-Laplacian operator. By applying the Linking Theorem and the Mountain Pass Theorem as well, the interaction of the nonlinearities with the first eigenvalue of fractional $p$-Laplacian will be used to prove existence and multiplicity of solutions.

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