Abstract
The concept of Lyapunov's function is an important tool in studying various problems of ordinary differential equations. In the present paper we shall extend the Lyapunov's method to study some problems of differential equations in Banach spaces. Continuing the theory of one parameter semi-groups of linear and bounded operators founded by Hille and Yoshida, Kato(4) presented some uniqueness and existence theorems for the solutions of linear differential equations of the typewhere A(t) is a given function whose values are linear operators in Banach space. Krasnoselskii, Krein and Soboleveskii (5,6) also considered such equations including non-linear differential equations of the typeMlak (9) obtained some results concerning the limitations of solutions of the latter equation.
Publisher
Cambridge University Press (CUP)
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