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 On discontinuous elliptic problems involving the fractional $p$-Laplacian in $\mathbb R^{N}$ Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1869-1889 https://doi.org/10.4134/BKMS.b171131Published online November 1, 2018 In Hyoun Kim, Yun-Ho Kim, Kisoeb Park Incheon National University, Sangmyung University, Incheon National University Abstract : We are concerned with the following fractional $p$-Laplacian inclusion: \begin{equation*} (-\Delta)_p^su+V(x)|u|^{p-2}u\in \lambda[\underline{f}(x,u(x)),\, \overline{f}(x,u(x))] \quad \rm{in} \ \ \mathbb R^{N}, \end{equation*} where $(-\Delta)_p^s$ is the fractional $p$-Laplacian operator, $0 Keywords : fractional$p\$-Laplacian, weak solution, critical point, degree theory MSC numbers : 35R11, 35J60, 47H11 Full-Text :