On periodic solutions of second-order differential equations with attractive–repulsive singularities

Sufficient conditions for the existence of a solution to the problem u ″ ( t ) = g ( t ) u μ ( t ) − h ( t ) u λ ( t ) + f ( t ) for a.e. t ∈ [ 0 , ω ] , u ( 0 ) = u ( ω ) , u ′ ( 0 ) = u ′ ( ω ) are established.