Abstract
ABSTRACTThe aim of this paper is to study the existence of solutions for the Kirchhoff-type equation involving nonlocal p-fractional Laplacian where is a non-local operator with singular kernel K, Ω is an open bounded subset of with Lipschitz boundary is a continuous function, M is a continuous function and f is a Carathéodory function which does not satisfy the Ambrosetti–Rabinowitz condition. By using Fountain Theorem, we obtain the existence of infinitely many solutions of the above problem. This result is an improvement of the result given by Yang and An. Furthermore, using the Morse theory, we get the existence of two solutions of the above problem. In our best knowledge, these results in this paper are new.
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