Monotone positive solutions of impulsive differential equations asymptotic to nonprincipal solutions

This study investigates the asymptotic behavior of monotone positive solutions for a general class of nonlinear second-order impulsive differential equations. By employing the principal and nonprincipal solutions of the associated homogeneous equation, we establish the existence of a monotone positive solution asymptotic to a nonprincipal solution at infinity. To achieve this, we also prove a compactness criterion for an effective use of Schauder’s fixed-point theorem. Under suitable conditions, similarly to the classical case, it is demonstrated that a monotone positive solution asymptotic to a nonprincipal solution exists. A concrete example is given to illustrate the results.