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On the Stability and Boundedness of Differential Systems†

Published online by Cambridge University Press:  24 October 2008

V. Lakshmikantham
V. Lakshmikantham
Affiliation:
Osmania University, Hyderabad and University of California, Los Angeles
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Extract

Consider the differential systems

where A(t), g(t, y) and g(t, y) are operators acting in the real Banach space E, A(t) is an unbounded, closed, linear operator for each t in 0 ≤ t < ∞ and x0, y0 belong to the domain of definition of the operator A (t0). Let ‖x‖ denote the norm of an element x ε: E and R(λ, t) the resolvent of A(t). Here and in the following the prime denotes the right-hand derivative.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 3 , July 1962 , pp. 492 - 496
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

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