Infinitely many solutions via critical points for a fractional p -Laplacian equation with perturbations

In this paper, we use variant fountain theorems to study the existence of infinitely many solutions for the fractional p -Laplacian equation (-Δ )_p^αu+λ V(x) | u | ^p-2u=f(x,u)-μ g(x) | u | ^q-2u, x∈ℝ^N, where λ,μ are two positive parameters, N,p≥ 2 , q∈ (1,p) , α∈ (0,1) , (-Δ )_p^α is the fractional p -Laplacian, and V,g,u:ℝ^N→ℝ , f:ℝ^N×ℝ→ℝ .