New Green's function and two infinite families of positive solutions for a second order impulsive singular parametric equation.

Using the theorem and properties of the fixed point index in a Banach space and applying a new method to dispose of the impulsive term, we prove that there exists a solvable interval of positive parameter λ in which the second order impulsive singular equation has two infinite families of positive solutions. Moreover, we also establish the new expression of Green's function for the above equation. Noticing that $\lambda>0$ and $c_{k}\neq0$ ( $k=1,2,\ldots,n$ ), our main results improve many previous results. This is probably the first time that the existence of two infinite families of positive solutions for second order impulsive singular parametric equations has been studied. [ABSTRACT FROM AUTHOR]