Stability theorems for some functional equations

Authors:
R. C. MacCamy and J. S. W. Wong

Journal:
Trans. Amer. Math. Soc. **164** (1972), 1-37

MSC:
Primary 45M05

MathSciNet review:
0293355

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Abstract | References | Similar Articles | Additional Information

Abstract: Functional-differential equations of the form

*g*an operator with domain in .

*g*may be unbounded.

*A*is called strongly positive if there exists a semigroup exp

*St*, where

*S*is symmetric and , such that

*St*is positive, that is,

*A*is strongly positive, and

*g*and

*f*are suitably restricted, then any solution which is weakly bounded and uniformly continuous must tend weakly to zero. Examples are given of both ordinary and partial differential-functional equations.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0293355-X

Keywords:
Functional-differential equation,
Gårding's inequality,
Laplace transform,
partial differential-functional equation,
positivity,
strong ellipticity,
strong positivity,
symmetric,
weak boundedness,
weak convergence,
weak stability,
weak uniform continuity

Article copyright:
© Copyright 1972
American Mathematical Society