Related papers: Period two solution for a class of distributed del…
We describe a variational approach to a notion of Hamiltonian delay equations. Our delay Hamiltonians are of product form. We consider several examples. For closed symplectically aspherical symplectic manifolds $(M,\omega)$ we prove that…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of…
In this work we study local oscillations in delay differential equations with a frequency domain methodology. The main result is a bifurcation equation from which the existence and expressions of local periodic solutions can be determined.…
In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for a hierarchy of integrable difference equations. We also provide an example of such a solution that is related to sequence generated…
For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have…
We study the set of T-periodic solutions of a class of T-periodically perturbed Differential-Algebraic Equations with separated variables. Under suitable hypotheses, these equations are equivalent to separated variables ODEs on a manifold.…
We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of…
Ordinary differential equations of the second order with one constant delay are considered in this paper. An analytical representation of the solution is obtained using the method of steps.
Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by…
The existence of elliptic periodic solutions of a perturbed Kepler problem is proved. The equations are in the plane and the perturbation depends periodically on time. The proof is based on a local description of the symplectic group in two…
By a new orthogonal direct sum decomposition $E_{M} = Y \oplus Z$, which $Z$ is related to $\Delta u_i(i=1,2,3,....,M)$, and a new functional $I(u)$, the method in [2] is improved to obtain new multiple periodic solutions with negativity…
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…
In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized Differential-Algebraic Equations with non-autonomous constraints of a particular type. We provide simple, degree theoretic…
This paper establishes an existence theory for distributed periodic solutions to Newton's equation with stochastic time-periodic forcing, where the friction matrix is the Hessian of a twice continuously differentiable friction function.…
A class of periodic differential $n$-dimensional systems with patch structure with (possibly infinite) delay and nonlinear impulses is considered. These systems incorporate very general nonlinearities and impulses whose signs may vary.…
Delay-differential equations are functional differential equations that involve shifts and derivatives with respect to a single independent variable. Some integrability candidates in this class have been identified by various means. For…
We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…
This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. We prove that…