Positive and oscillating solutions of equation
An existence criterion of positive solutions of -type retarded functional differential equations
Solutions of a singular Cauchy problem for a nonlinear system of differential equations
Asymptotic behaviour of solutions of linear discrete equations
Subdominant positive solutions of the discrete equation .
Multipoint singular boundary-value problem for systems of nonlinear differential equations.
On connection between second-order delay differential equations and integrodifferential equations with delay.
A criterion for convergence of solutions of homogeneous delay linear differential equations
The linear homogeneous differential equation with variable delays is considered, where , I = [t₀,∞), ℝ⁺ = (0,∞), on I, the functions , j=1,...,n, are increasing and the delays are bounded. A criterion and some sufficient conditions for convergence of all solutions of this equation are proved. The related problem of nonconvergence is also discussed. Some comparisons to known results are given.
Asymptotic behaviour of solutions of linear differential equations with delay
Inequalities for some positive solutions of the linear differential equation with delay ẋ(t) = -c(t)x(t-τ) are obtained. A connection with an auxiliary functional nondifferential equation is used.
Behaviour of solutions of linear differential equations with delay
This contribution is devoted to the problem of asymptotic behaviour of solutions of scalar linear differential equation with variable bounded delay of the form with positive function Results concerning the structure of its solutions are obtained with the aid of properties of solutions of auxiliary homogeneous equation where the function is positive. A result concerning the behaviour of solutions of Eq. (*) in critical case is given and, moreover, an analogy with behaviour of solutions of...
The singular Cauchy-Nicoletti problem for the system of two ordinary differential equations
In the paper the singular Cauchy-Nicoletti problem for the system ot two ordinary differential equations is considered. New sufficient conditions for solvability of this problem are proved. In the proofs the topological method is applied. Some comparisons with known results are also given in the paper.
Inequalities for solutions of systems with “pure” delay
Asymptotical convergence of the solutions of a linear differential equation with delays.
On the critical case in oscillation for differential equations with a single delay and with several delays.
Stability of nonlinear autonomous quadratic discrete systems in the critical case.
One case of appearance of positive solutions of delayed discrete equations
When mathematical models describing various processes are analysed, the fact of existence of a positive solution is often among the basic features. In this paper, a general delayed discrete equation is considered. Sufficient conditions concerning are formulated in order to guarantee the existence of a positive solution for . An upper estimate for it is given as well. The appearance of the positive solution takes its origin in the nature of the equation considered since the results hold only...
Existence of positive solutions of -dimensional system of nonlinear differential equations entering into a singular point
Asymptotic estimation of the convergence of solutions of the equation
The main result of the present paper is obtaining new inequalities for solutions of scalar equation . Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution reaches an - neighbourhood of origin and remains in it.
Convergence tests for one scalar differential equation with vanishing delay
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