文档介绍：Differential Calculus
Newton and Leibniz,quite independently of one another,were largely responsible for developing the ideas of integral calculus to the point where hitherto insurmountable problems could be solved by more or less routine successful accomplishments of these men were primarily due to the fact that they were able to fuse together the integral calculus with the second main branch of calculus,differential calculus.
In this article, we give sufficient conditions for controllability of some partial neutral functional differential equations with infinite delay. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. The results are obtained using the integrated semigroups theory. An application is given to illustrate our abstract result.
Key words Controllability; integrated semigroup; integral solution; infinity delay
1 Introduction
In this article, we establish a result about controllability to the following class of partial neutral functional differential equations with infinite delay:
(1)
where the state variabletakes values in a Banach spaceand the control is given in ,the Banach space of admissible control functions with U a Banach space. C is a bounded linear operator from U into E, A : D(A) ⊆ E → E is a linear operator on E, B is the phase s