Gap-bifurcation for nonlinear perturbations of Hill's equation.
Generic bifurcation of reversible vector fields on a 2-bidimensional manifold.
In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.
Generic saddle-node bifurcation for cascade second order ODEs on manifolds
Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.
Global behavior of the components for the second order -point boundary value problems.
Global bifurcation for second-order Neumann problem with a set-valued term.
Global bifurcation from the Fučik spectrum
Global homoclinic bifurcation for damped systems.
Global qualitative investigation, limit cycle bifurcations and Applications of Polynomial Dynamical Systems
Global structure of nodal solutions for second-order -point boundary value problems with superlinear nonlinearities.
Guidance properties of a cylindrical defocusing waveguide
We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification is such that...