摘要：In this paper, we deal with the fractional Laplacian equations ( P ) { ( − Δ ) s u = f ( x , u ) , x ∈ Ω , u ( x ) = 0 , x ∈ R N ∖ Ω , $$(\mathrm{P})\quad \left \{ \textstyle\begin{array}{@{}l@{\quad}l} (-\Delta)^{s} u = f(x,u), & x\in \Omega,\\ u(x)= 0, & x\in \mathbb{R}^{N}\backslash\Omega, \end{array}\displaystyle \right . $$ where 0 2 s $N\in\mathbb{N}, N>2s$ , Ω ⊂ R N $\Omega\subset \mathbb{R}^{N}$ is a bounded domain with smooth boundary. Under local growth conditions of f ( x , t ) $f(x,t)$ , infinitely many solutions for problem (P) are obtained via variational methods.
