For general matrix summability methods, we find necessary and sufficient conditions for such methods to be stronger than multisummability. In a second part we show the existence of power series which are not multisummable but can be summed by a matrix method satisfying the conditions mentioned above
In this work, we present necessary and sufficient conditions for oscillation of all solutions of a second-order functional differential equation of type where . Under the assumption , we consider two cases when and . Our main tool is Lebesgue’s dominated convergence theorem. Finally, we provide examples illustrating our results and state an open problem.
In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.
In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form , where is a quotient of odd positive integers, in the superlinear case and in the sublinear case .
An optimal control problem is studied for a Lotka-Volterra system of three differential equations. It models an ecosystem of three species which coexist. The species are supposed to be separated from each others. Mathematically, this is modeled with the aid of two control variables. Some necessary conditions of optimality are found in order to maximize the total number of individuals at the end of a given time interval.