Measure differential equation with a nonlinear growth/decay term

In this paper we obtain an existence result for a measure differential equation with nonlinear growth/decay term that may change the sign. This generalizes model setting proposed by Piccoli and Rossi to applications in life sciences describing example birth/death processes of individuals. The proof requires modification approximating schemes introduced original Rossi. new scheme combines discretization exponential solution term, hence, preserves nonnegativity measure. Furthermore, formulate analytic condition on vector field, which substantially simplifies previous continuity solutions respect initial data while simultaneously generalizing former formulated