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 Existence, multiplicity and regularity of solutions for the fractional p-Laplacian equation J. Korean Math. Soc.Published online February 27, 2020 Yun-Ho Kim Sangmyung University Abstract : We are concerned with the following elliptic equations: \begin{equation*} \begin{cases} (-\Delta)_p^su=\lambda f(x,u) \quad \text{in} \ \ \Omega,\\ u= 0\quad \text{on}\ \ \mathbb{R}^N\backslash\Omega, \end{cases} \end{equation*} where $\lambda$ is real parameter, $(-\Delta)_p^s$ is the fractional $p$-Laplacian operator, \$0