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Existence of nontrivial solutions for singular quasilinear equations with sign changing nonlinearity.

By an application of Bonanno’s three critical point theorem, we establish the existence of a nontrivial solution to the problem 
−∆p u = μ g(x)|u|p−2 u + λa(x)f (u) |x|p u = 0 on ∂Ω, 
in Ω, under some restrictions on g, a and f for certain positive values of μ and λ.