Abstract

Chapter 8 deals with nonoscillation problems for a scalar linear delay differential equation of the second order including explicitly a term with the first derivative which is usually called “a damping term”. Most of publications deal with equations not containing the term with the first derivative; for these equations, positivity of the coefficients and a solution on the semiaxis implies that its derivative is nonnegative. This fact is very important, and it is employed in most investigations on second-order delay differential equations. If the first derivative is included in the equation explicitly, i.e. the equation contains the damping term, then a sign of a solution does not uniquely define the sign of its derivative, which makes the study of oscillation properties of the equations with the damping term more complicated. This is the reason why such equations are much less studied than equations without the damping term.

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