Holomorphic solutions to linear first-order functional differential equations.
Homoclinic and period-doubling bifurcations for damped systems
Homoclinic and periodic solutions of scalar differential delay equations
Homoclinic, Heteroclinic, and Periodic Orbits for a Class of Indefinite Hamiltonian Systems.
Homoclinic orbits and Lie rotated vector fields.
Homoclinic orbits for a class of infinite dimensional hamiltonian systems
Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
We consider a conservative second order Hamiltonian system in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
Homoclinic orbits for a class of symmetric Hamiltonian systems.
Homoclinic orbits for an almost periodically forced singular Newtonian system in ℝ³
This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in ℝ³ which are subjected to almost periodic forcing in time variable.
Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems
Homoclinic solutions for a class of second order non-autonomous systems.
Homoclinic solutions for linear and linearizable ordinary differential equations.
Homoclinic solutions for second-order non-autonomous Hamiltonian systems without global Ambrosetti-Rabinowitz conditions.
Homoclinic solutions of 2nth-order difference equations containing both advance and retardation
By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.
Homoclinic solutions of singular nonautonomous second-order differential equations.
Homogene lineare zu sich selbst begleitende Differentialgleichung zweiter Ordnung
Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.
Let X be a homogeneous polynomial vector field of degree 2 on S2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S2, and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. Moreover, we show that if X has at least an invariant circle then it does not have limit cycles.
Homogeneous systems of higher-order ordinary differential equations
The concept of homogeneity, which picks out sprays from the general run of systems of second-order ordinary differential equations in the geometrical theory of such equations, is generalized so as to apply to equations of higher order. Certain properties of the geometric concomitants of a spray are shown to continue to hold for higher-order systems. Third-order equations play a special role, because a strong form of homogeneity may apply to them. The key example of a single third-order equation...
Homogeneous Systems with a Quiescent Phase
Recently the effect of a quiescent phase (or dormant/resting phase in applications) on the dynamics of a system of differential equations has been investigated, in particular with respect to stability properties of stationary points. It has been shown that there is a general phenomenon of stabilization against oscillations which can be cast in rigorous form. Here we investigate, for homogeneous systems, the effect of a quiescent phase, and more generally, a phase with slower dynamics. We show that...
Homogenization and correctors for nonlinear elliptic equations