Multiple solutions of a nonlocal system with singular nonlinearities

In this work, we study the fractional Laplacian equation with singular nonlinearity: 'Greek Passage', where ω is a bounded domain in ℝn with smooth boundary ∂Ω, N > 2s, s ∈ (0, 1), 0 < α < 1, 0 < β < 1, 1 < q < 2 < 2s∗, 2s∗ = 2N/N-2s is the fractional Sobolev exponent, λ,μ are two parameters, a,b,c ∈ C(Ω¯) are nonnegative weight functions, and (-Δ)s is the fractional Laplace operator. We use the Nehari manifold approach and some variational techniques in order to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ and μ.