Existence of solutions for non-coercive variational-hemivariational inequalities involving the nonlocal fractional p-Laplacian

In this paper, we study the existence of solutions for non-coercive variational-hemivariational inequalities involving nonlocal fractional p-Laplacian. Our approach is based on the theory of pseudomonotone operators in the sense of Brézis, recession analysis and the properties of nonlocal fractional p-Laplace operators recently established.The innovation of this paper is that we do not assume the usual coercivity or smallness assumptions as stated in most existing literature. The absence of such assumptions will make the existence of solutions very complicated. We have to proceed from the specific problem itself and seek specific methods based on the inherent characteristics of different problems.