Regular Article
Nonoscillation for Functional Differential Equations of Mixed Type

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Abstract

An example is given to show that the linear autonomous functional differential equation of mixed type (t) + 1 1[dμ(s)]x(t + s) = 0 may have a nonoscillatory solution in spite of the nonexistence of real roots of its characteristic equation. Under a regularity condition on μ at 1, exponential boundedness and asymptotic expansions are obtained for the nonoscillatory solutions.

Keywords

mixed type functional differential equation
nonoscillation
characteristic equation
asymptotic expansion

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Submitted by Hal, L. Smith

f1

[email protected]

1

Partially supported by the Hungarian Foundation for Scientific Research, Grant T/029188.