
It is considered the linear autonomous functional-differential equation \[ \dot x(t)+ \int^1_{-1} (d\mu(s)) x(t+ s)= 0 \] which is of mixed (retarted/advanced) type. An example shows that such equations may be nonoscillatory in spite of the existence of the real roots of the characteristic equation. Exponential estimates and boundedness are analyzed. It is shown that nonoscillatory solutions may be bounded even without exponential bounds for all solutions.
nonoscillation, asymptotic expansion, Growth, boundedness, comparison of solutions to functional-differential equations, Oscillation theory of functional-differential equations, nonoscillatory solutions, Applied Mathematics, Linear functional-differential equations, mixed type functional differential equation, characteristic equation, linear autonomous functional-differential equation, Analysis
nonoscillation, asymptotic expansion, Growth, boundedness, comparison of solutions to functional-differential equations, Oscillation theory of functional-differential equations, nonoscillatory solutions, Applied Mathematics, Linear functional-differential equations, mixed type functional differential equation, characteristic equation, linear autonomous functional-differential equation, Analysis
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