Sign changing Lyapunov functions and perturbation of invariant tori of dynamical systems
Singular integral inequalities and stability of semilinear parabolic equations
Using a method developed by the author for an analysis of singular integral inequalities a stability theorem for semilinear parabolic PDEs is proved.
Singular perturbation for nonlinear boundary-value problems.
Singular perturbation for the Dirichlet boundary control of elliptic problems
A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small...
Singular perturbation for the Dirichlet boundary control of elliptic problems
A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small...
Singular perturbations in foliations.
Singular solutions for the differential equation with -Laplacian
In the paper a sufficient condition for all solutions of the differential equation with -Laplacian to be proper. Examples of super-half-linear and sub-half-linear equations , are given for which singular solutions exist (for any , , ).
Singular solutions of a singular differential equation.
Singularité analytique et perturbation singulière en dimension 2
Singularities of vector fields
Slow and fast systems with Hamiltonian reduced problems.
Smoothness property for bifurcation diagrams.
Strata of bifurcation sets related to the nature of the singular points or to connections between hyperbolic saddles in smooth families of planar vector fields, are smoothly equivalent to subanalytic sets. But it is no longer true when the bifurcation is related to transition near singular points, for instance for a line of double limit cycles in a generic 2-parameter family at its end point which is a codimension 2 saddle connection bifurcation point. This line has a flat contact with the line...
Solutions approaching polynomials at infinity to nonlinear ordinary differential equations.
Solutions d'une equation differentielle au deuxieme membre factorise dans les voisinages des fonctions donnees et leur stabilite
Solutions to Lyapunov stability problems: Nonlinear systems with continuous motions.
Solutions to Lyapunov stability problems of sets: Nonlinear systems with differentiable motions.
Solving a collection of free coexistence-like problems in stability
Some classes of linear th-order differential equations
Sufficient conditions for the -th order linear differential equation are derived which guarantee that its Cauchy function , together with its derivatives , , is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.
Some new results in 1D inverse scattering
Some oscillatory properties of the perturbed linear differential equations of order
In this paper there are generalized some results on oscillatory properties of the binomial linear differential equations of order ) for perturbed iterative linear differential equations of the same order.