Stability in terms of two measures for population growth models with impulsive perturbations

In this paper, we establish some criteria for the stability of trivial solution of population growth models with impulsive perturbations. The working tools are based on the theory of generalized ordinary differential equations. Here, the conditions concerning the functions are more general than the classical ones.

On the solvability of the modified Cauchy problem for linear systems of generalized ordinary differential equations with singularities

Effective sufficient conditions are given for the unique solvability of the Cauchy problem for linear systems of generalized ordinary differential equations with singularities.

Results on Uniqueness of Solution of Nonhomogeneous Impulsive Retarded Equation Using the Generalized Ordinary Differential Equation

In this work, we consider an initial value problem of a nonhomogeneous retarded functional equation coupled with the impulsive term. The fundamental matrix theorem is employed to derive the integral equivalent of the equation which is Lebesgue integrable. The integral equivalent equation with impulses satisfying the Carathéodory and Lipschitz conditions is embedded in the space of generalized ordinary differential equations (GODEs), and the correspondence between the generalized ordinary differential equation and the nonhomogeneous retarded equation coupled with impulsive term is established by the construction of a local flow by means of a topological dynamic satisfying certain technical conditions. The uniqueness of the equation solution is proved. The results obtained follow the primitive Riemann concept of integration from a simple understanding.