On a time nonlocal problem for inhomogeneous evolution equations
In this paper, the authors study the solvability of the nonlocal problem for the inhomogeneous differential evolution equation in Banach space, in which the main operator generates a strongly continuous semigroup and the determining solution is given by an integral condition in the sense of Stieltjes. They obtain necessary and sufficient conditions for the existence of a generalized solution for the problem, which depends on whether the nonlocal data belong to the generator domain. Moreover, they give some conditions for the existence of the classical solution of the nonlocal problem. Furthermore, they extend these result to a Sobolev-type linear equation in Banach space, which has a degenerate operator at the derivative. Finally, they give an example to illustrate the application of the result.
scientific article; zbMATH DE number 6381107
scientific article