Related papers: Periodic solutions of second order Hamiltonian sys…
In this work we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the form \begin{equation*} y(t+2)+by(t+1)+cy(t)=g(t,y(t)) \end{equation*} where $c\neq 0$, and…
We prove an index theorem for families of linear periodic Hamiltonian systems, which is reminiscent of the Atiyah-Singer index theorem for selfadjoint elliptic operators. For the special case of one-parameter families, we compare our…
We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
A linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrodinger-Hirota equation. Optimal, second order convergence in the discrete $H^1-$norm is proved,…
We show that su(2) rational and trigonometric Gaudin models, or in other words, generalised coupled angular momenta systems, have singularities that undergo Hamiltonian Hopf bifurcations. In particular, we find a normal form for the…
We study the existence of families of periodic solutions in a neighbourhood of a symmetric equilibrium point in two classes of Hamiltonian systems with involutory symmetries. In both classes, involutions reverse the sign of the Hamiltonian…
In this paper we evaluate the topological index of periodic solutions otained via the Malkin-Loud bifurcation result. Incidentally, we do not assume that the perturbation is differentiale.
In this paper, we prove the existence of periodic solutions with any prescribed minimal period $T>0$ for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of…
The purpose of this paper is to study properties of continua (closed connected sets) of nontrivial solutions of non-cooperative elliptic systems considered on geodesic balls in $S^n$. In particular, we have shown that if the geodesic ball…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
This paper is devoted to the study of periodic solutions of Hamiltonian system $\dot z(t)=J \nabla H(z(t))$, where $H$ is symmetric under an action of a compact Lie group. We are looking for periodic solutions in a nearby of non-isolated…
Ordinary differential equations of the first order on the torus have been investigated in detail by H. Poincar\'e and A. Denjoy. The long-standing problem of generalising these results for the equations of the order $k>1$ (or for the…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
In our previous paper: Integrability of Homogeneous potentials of degree $k = \pm 2$. An application of higher order variational equations, we tried to extract some particular structures of the higher variational equations (the ${VE}_p$ for…
We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems,…
In this paper we investigate the existence and uniqueness of bounded, periodic and almost periodic solutions for second order differential equations involving reflection of the argument.The relationship between frequency modules of forced…
In this paper we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second order coupled systems of differential equations on the real line. We point out that it is required only conditions on the…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…