Nonoscillation for Functional Differential Equations of Mixed Type

Abstract An example is given to show that the linear autonomous functional differential equation of mixed type ẋ(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.

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