Asymptotic convergence criteria of solutions of delayed functional differential equations. (English) Zbl 1025.34062

The author studies the scalar equation \(\dot x=f(t,x_t)\) under the assumption that every constant is its solution. Criteria and sufficient conditions for the convergence of solutions are found. It is proved that all solutions are convergent if and only if there exists at least one increasing and convergent solution. As application, criteria for some classes of linear and nonlinear equations are obtained.


34K07 Theoretical approximation of solutions to functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K05 General theory of functional-differential equations
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