Необходимые и достаточные условия для колебательных функциональных дифференциальных уравнений

Аңдатпа

In this survey, necessary and sufficient conditions for the oscillation of solutions of retarded, advanced
and neutral differential equations of first and higher order with one or several constant
coefficients and constant arguments, in terms of the characteristic equation, are presented. Explicit
(in terms of the constant coefficient and constant argument only) necessary and sufficient
conditions are also presented in the case of one argument. In the case of nth order equations necessary
and sufficient conditions for the oscillation of all solutions are presented when n is odd, while
necessary and sufficient conditions for the oscillation of all bounded solutions are presented when
n is even. In this case explicit sufficient conditions for the oscillation of all solutions are presented
when n is odd, while explicit sufficient conditions for the oscillation of all bounded solutions for
retarded equations and of all unbounded solutions for advanced equations are presented when n
is even. In the case of several arguments explicit but sufficient conditions only are given and the
results are also extended to equations with several variable coefficients.