Nonoscillation for functional differential equations of mixed type. (English) Zbl 0955.34054

Krisztin, Tibor

J. Math. Anal. Appl. 245, No. 2, 326-345 (2000).

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.

Reviewer: Vladimir Răsvan (Craiova)

MSC:

34K11	Oscillation theory of functional-differential equations
34K12	Growth, boundedness, comparison of solutions to functional-differential equations
34K06	Linear functional-differential equations

Keywords:

linear autonomous functional-differential equation; nonoscillatory solutions

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