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×_K2$K_1\times K_2$, 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×_K2$K_1\times K_2$, 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.