Asymptotic stability of solutions of a class of systems of nonlinear differential equations with delay

We study systems of differential equations with delay whose right-hand sides are represented as sums of potential and gyroscopic components of vector fields. We assume that in the absence of a delay zero solutions of considered systems are asymptotically stable. By the Lyapunov direct method, using the Razumikhin approach, we prove that in the case of essentially nonlinear equations the asymptotic stability of zero solutions is preserved for any value of the delay.     

Convergence of bounded solutions for a class of systems of delay differential equations

In this paper, the convergence of a class of systems of delay differential equations is considered. We show that every bounded solution of such systems tends to an equilibrium under certain hypotheses. Our results extend some corresponding ones already known.     

Chaotic behavior of a class of nonlinear differential delay equations

Summary For the differential delay equation the existence of infinitely many periodic as well as infinitely many aperiodic solutions («choatic behavior in the sense of Li and Yorke») is proved.     

Positive periodic solutions for a class of nonlinear delay equations

Applying the theory of topological degree, sufficient and realistic conditions are obtained for the existence of positive periodic solutions of a class of neutral delays equation. From those conditions, an algebraic criterion of existence for a more general neutral Lotka–Volterra equation with several delays is obtained, which extends and improves the previous results. In addition, this method is of great interest in many applications such as biomathematics.     

Positive periodic solutions for a class of delay differential equations

In this paper, we employ fixed point theorem and functional equation theory to study the existence of positive periodic solutions of the delay differential equation

x^′(t)=α(t)x(t)-β(t)x²(t)+γ(t)x(t-τ(t))x(t).     

Periodic solutions for a class of non-autonomous differential delay equations

By applying symplectic transformation, Floquet theory and some results in critical point theory, we establish the existence of periodic solutions for a class of non-autonomous differential delay equations, which can be changed to Hamiltonian systems.     

Flow invariance for solutions to nonlinear nonautonomous partial differential delay equations

We investigate the problem of existence and flow invariance of mild solutions to nonautonomous partial differential delay equations , t?s, us=φ, where B(t) is a family of nonlinear multivalued, α-accretive operators with D(B(t)) possibly depending on t, and the operators F(t,.) being defined—and Lipschitz continuous—possibly only on “thin” subsets of the initial history space E. The results are applied to population dynamics models. We also study the asymptotic behavior of solutions to this equation. Our analysis will be based on the evolution operator associated to the equation in the initial history space E.     

On the properties of solutions to a class of nonlinear systems of differential equations of large dimension

We consider the Cauchy problem for a class of nonlinear systems of differential equations of large dimension, establish some properties of solutions, and prove that for a sufficiently large number of differential equations the last component of the solution is an approximate solution to the initial value problem for a delay differential equation.     

Existence of positive solutions of nonlinear fractional delay differential equations

This paper investigates the existence and uniqueness of positive solutions for a class of nonlinear fractional delay differential equations. Using a nonlinear alternative of Leray-Schauder type, we show the existence of positive solutions for the equations in question.     

Global existence of solutions for a class of nonlinear differential equations

By making use of a special Lyapunov-type function and applying the comparison method due to Conti, we prove global existence of solutions for a general class of nonlinear second-order differential equations that includes, in particular, van der Pol, Rayleigh, and Liénard equations, widely encountered in applications. Relevant examples are discussed.     

Some properties of solutions for a class of nonlinear differential equations

In this paper, we will consider integrability properties for the solutions of the following class of nonlinear differential equations: wheref has a logarithmic behaviour at infinity.

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Sunto In questo lavoro si studiano proprietà di integrabilità per le soluzioni della seguente classe di equazioni differenziali nonlineari dovef ha un comportamento logaritmico all'infinito.