Bounded solutions for second-order ordinary differential equations.
Boundedness and global stability for a predator-prey system with the Beddington-DeAngelis functional response.
Boundedness and oscillatoriness of solutions of the equation y" + a(x)g(y, y') + b(x)f(y)h(y') = 0
Boundedness and square integrability of solutions of certain third-order differential equations
We establish some new sufficient conditions which guarantee the boundedness and square integrability of solutions of certain third order differential equation. Example is included to illustrate the results. By this work, we extend and improve some results in the literature.
Cauchy problem for derivors in finite dimension.
Cesaro asymptotic equipartition of energy in the coupled case.
Comparison theorems for noncanonical third order nonlinear differential equations
The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.
Comparison theorems for nonlinear ODE's
Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems
MSC 2010: 26A33, 34D05, 37C25In the paper, long-time behavior of solutions of autonomous two-component incommensurate fractional dynamical systems with derivatives in the Caputo sense is investigated. It is shown that both the characteristic times of the systems and the orders of fractional derivatives play an important role for the instability conditions and system dynamics. For these systems, stationary solutions can be unstable for wider range of parameters compared to ones in the systems with...
Connection between asymptotic properties and zeros of solutions of
Consensus of a two-agent system with nonlinear dynamics and time-varying delay
To explore the impacts of time delay on nonlinear dynamics of consensus models, we incorporate time-varying delay into a two-agent system to study its long-time behaviors. By the classical 3/2 stability theory, we establish a sufficient condition for the system to experience unconditional consensus. Numerical examples show the effectiveness of the proposed protocols and present possible Hopf bifurcations when the time delay changes.
Continuability, boundedness, and convergence to zero of solutions of a perturbed nonlinear ordinary differential equation
Contributions of Alan C. Lazer to mathematical population dynamics.
Contributions to the asymptotic behaviour of the equation with a complex-valued function
Convergence of solutions for a fifth-order nonlinear differential equation.
Convergence of solutions of certain fourth-order nonlinear differential equations.
Convergence of solutions of certain non-homogeneous third order ordinary differential equations
Coppel-Conti sets of linear systems.
Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity
This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation , by means of regularly varying functions, where is a positive constant and is a positive continuous function on . It is shown that if is a regularly varying function, then it is possible to establish necessary and sufficient conditions for the existence of slowly varying solutions and regularly varying solutions of (A) which decrease to as and to acquire...
Decoupling normalizing transformations and local stabilization of nonlinear systems
The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given.