5 research outputs found
Periodic bifurcation problems for fully nonlinear neutral functional differential equations via an integral operator approach: the multidimensional degeneration case
We consider a -periodically perturbed autonomous functional differential equation of neutral type. We assume the existence of a -periodic limit cycle for the unperturbed autonomous system. We also assume that the linearized unperturbed equation around the limit cycle has the characteristic multiplier of geometric multiplicity and algebraic multiplicity greater than~. The paper deals with the existence of a branch of -periodic solutions emanating from the limit cycle. The problem of finding such a branch is converted into the problem of finding a branch of zeros of a~suitably defined bifurcation equation \hbox{.} The main task of the paper is to define a novel equivalent integral operator having the property that the -periodic adjoint Floquet solutions of the unperturbed linearized operator correspond to those of the equation , . Once this is done it is possible to express the condition for the existence of a branch of zeros for the bifurcation equation in terms of a multidimensional Malkin bifurcation function
Existence principles for inclusions of Hammerstein type involving noncompact acyclic multivalued maps
We apply Monch type fixed point theorems for acyclic multivalued maps to the solvability of inclusions of Hammerstein type in Banach spaces. Our approach makes possible to unify and improve the existence theories for nonlinear evolution problems and abstract integral inclusions of Volterra and Fredholm type
Theme 4 | Simulation et optimisation de systemes complexes
This paper deals with nonlinear feedback stabilization problem of a #exible beam clamped at a rigid body and free at the other end. We assume that there is no damping. The feedbacklaw proposed here consists of a nonlinear control torque applied to the rigid body and either a nonlinear boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends thelinear case studied by Laousy et al. to a more general class of controls. This new class of controls is in particular of the interest to be robust
Cauchy problem for derivors in finite dimension
In this paper we study the uniqueness of solutions to ordinary differential equations which fail to satisfy both accretivity condition and the uniqueness condition of Nagumo, Osgood and Kamke. The evolution systems considered here are governed by a continuous operators defined on such that is a derivor; i.e., is quasi-monotone with respect to