Systems of differential equations in the Lebesgue spaces

Abstract

Herein, we investigate systems of nonautonomous differential equations with generalized coefficients using the algebra of new generalized functions. We consider a system of nonautonomous differential equations with generalized coefficients as a system of equations in differentials in the algebra of new generalized functions. The solution of such a system is a new generalized function. It is shown that the different interpretations of the solutions of the given systems can be described by a unique approach of the algebra of new generalized functions. In this paper, for the first time in the literature, we describe associated solutions of the system of nonautonomous differential equations with generalized coefficients in the Lebesgue spaces L (T) p with functions that satisfy the linear growth condition.