LAUSR

AbstractIn this paper, we use variant fountain theorems to study the existence of infinitely many solutions for the fractional p-Laplacian equation (−Δ)pαu+λV(x)|u|p−2u=f(x,u)−μg(x)|u|q−2u,x∈RN,$$ (-\Delta )_{p}^{\alpha }u+\lambda V(x) \vert u \vert ^{p-2}u=f(x,u)-\mu g(x) \vert u \vert ^{q-2}u,\quad x\in \mathbb{R}^{N}, $$ where λ,μ$\lambda,\mu $ are two positive parameters, N,p≥2$N,p\ge 2$, q∈(1,p)$q\in (1,p)$, α∈(0,1)$\alpha \in (0,1)$, (−Δ)pα$(-\Delta )_{p}^{\alpha }$ is the fractional p-Laplacian, and V,g,u:RN→R$V,g,u:\mathbb{R}^{N}\to \mathbb{R}$, f:RN×R→R$f:\mathbb{R}^{N}\times \mathbb{R}\to \mathbb{R}$.