Existence and Multiplicity of Solutions for a Periodic Hill's Equation with Parametric Dependence and Singularities

We deal with the existence and multiplicity of solutions for theperiodic boundary value problem x″(t)+a(t)x(t)=λg(t)f(x)+c(t), x(0)=x(T), x′(0)=x′(T), where λ is a positive parameter. The function f:(0,∞)→(0,∞) is allowed to be singular, and the related Green's function is nonnegativeand can vanish at some points