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 Existence of weak solutions to a class of Schr\"{o}dinger type equations involving the fractional $p$-Laplacian in $\mathbb R^{N}$ J. Korean Math. Soc. 2019 Vol. 56, No. 6, 1529-1560 https://doi.org/10.4134/JKMS.j180785Published online November 1, 2019 Jae-Myoung Kim, Yun-Ho Kim, Jongrak Lee Andong National University; Sangmyung University; Ewha Womans University Abstract : We are concerned with the following elliptic equations: \begin{equation*} (-\Delta)_p^su+V(x)|u|^{p-2}u=\lambda g(x,u) \quad \textmd{in} \quad \mathbb R^{N}, \end{equation*} where $(-\Delta)^s_p$ is the fractional $p$-Laplacian operator with $0 Keywords : fractional$p\$-Laplacian, variational methods, critical point theory MSC numbers : 35R11, 35A15, 35J60, 49R05 Downloads: Full-text PDF   Full-text HTML