Stability theorems for some functional equations
Authors:
R. C. MacCamy and J. S. W. Wong
Journal:
Trans. Amer. Math. Soc. 164 (1972), 137
MSC:
Primary 45M05
MathSciNet review:
0293355
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Abstract: Functionaldifferential equations of the form are considered. Here is to be an element of a Hilbert space a family of bounded symmetric operators on and 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, for all smooth . It is shown that if 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 differentialfunctional equations.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719720293355X
PII:
S 00029947(1972)0293355X
Keywords:
Functionaldifferential equation,
Gårding's inequality,
Laplace transform,
partial differentialfunctional equation,
positivity,
strong ellipticity,
strong positivity,
symmetric,
weak boundedness,
weak convergence,
weak stability,
weak uniform continuity
Article copyright:
© Copyright 1972
American Mathematical Society
