Positive solutions of two-point boundary value problems for systems of nonlinear second-order singular and impulsive differential equations

This paper is devoted to the study of multiple and single positive solutions of two-point boundary value problems for nonlinear second-order singular and impulsive differential systems. By constructing a cone K1×K2K1×K2, which is the Cartesian product of two cones in the space C[0,1]C[0,1], and computing the fixed-point index in the K1×K2K1×K2, we establish the conditions for the existence of at least one or at least two positive solutions to two-point boundary value problems for systems of nonlinear second-order singular and impulsive differential equations.