On Optimal Controls for Measure Delay-Differential Equations

Nonlinear Integral Equations in a Measure Space

“…By b.v. we denote "bounded variation". Here, by a solution, we mean a function of bounded variation satisfying equation (2). We consider the equation (6), instead of equation (2).…”

“…Here, by a solution, we mean a function of bounded variation satisfying equation (2). We consider the equation (6), instead of equation (2). For equation (6) all the conditions of Theorem 1 are verified by maintaining a and U as such and putting LM=N.…”

“…In fact we can formulate the following theorem for equation (2) for the existence of its solution. By b.v. we denote "bounded variation".…”

“…We note that we can consider [f0, oo) instead of [t0, tx]. Conversely if (6) has a solution, the steps can be retraced back and we get a solution of equation (2).…”

“…In §2, a link between these equations and equations from which this abstraction was made is established. It is to be noted that differential equations containing measures considered in [1], [2], [4], [6] and their abstraction in [5] from the point of view of existence of solutions are particular cases of the class of equations considered here. The whole idea in this abstraction is to free the differential and integral equations of implicit Cartesian co-ordinate system.…”