Completely monotone families of solutions of -th order linear differential equations and infinitely divisible distributions
Computable error bounds for collocation methods.
Computing generalized inverse systems using matrix pencil methods
We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil...
Computing the differential of an unfolded contact diffeomorphism
Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of . Singularity classes containing bifurcation points with , are considered.
Computing the Galois group of a linear differential equation
Concours d'admission à l'École normale supérieure
Conditional differential equations
We introduce and study conditional differential equations, a kind of random differential equations. We give necessary and sufficient conditions for the existence of a solution of such an equation. We apply our main result to a Malthus type model.
Conditioning of three-point boundary value problems associated with first order matrix Lyapunov systems.
Conditions for convergence of the fundamental matrix of linear time-invariant time-delayed singular systems.
Conditions for the absence of positive solutions of a first order differential inequality with a single delay
A sufficient integral condition for the absence of eventually positive solutions of a first order stable type differential inequality with one nondecreasing retarded argument is given. In the special case of equality the result becomes an oscillation criterion.
Conditions for the integrability of a second order nonlinear differential equation.
Conditions for the Integrability of Second Order Nonlinear Differential Equation, II
Cone-valued impulsive differential and integrodifferential inequalities.
Conflict-Controlled Processes Involving Fractional Differential Equations with Impulses
MSC 2010: 34A08, 34A37, 49N70Here we investigate a problem of approaching terminal (target) set by a system of impulse differential equations of fractional order in the sense of Caputo. The system is under control of two players pursuing opposite goals. The first player tries to bring the trajectory of the system to the terminal set in the shortest time, whereas the second player tries to maximally put off the instant when the trajectory hits the set, or even avoid this meeting at all. We derive...
Conformal structures associated to generic rank 2 distributions on 5-manifolds -- characterization and Killing-field decomposition.
Conjugacy and disconjugacy criteria for second order linear ordinary differential equations
Conjugacy and disconjugacy criteria are established for the equation where is a locally summable function.
Conjugate points of solutions of a fourth-order iterated linear differential equation
Conjugate points of solutions of an iterated differential equation of the -th order
Conjugation to a shift and the splitting of invariant manifolds
We give sufficient conditions for a diffeomorphism in the plane to be analytically conjugate to a shift in a complex neighborhood of a segment of an invariant curve. For a family of functions close to the identity uniform estimates are established. As a consequence an exponential upper estimate for splitting of separatrices is established for diffeomorphisms of the plane close to the identity. The constant in the exponent is related to the width of the analyticity domain of the limit flow separatrix....
Conley type index and Hamiltonian inclusions
This paper is based mainly on the joint paper with W. Kryszewski [Dzedzej, Z., Kryszewski, W.: Conley type index applied to Hamiltonian inclusions. J. Math. Anal. Appl. 347 (2008), 96–112.], where cohomological Conley type index for multivalued flows has been applied to prove the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian inclusions. Some proofs and additional remarks concerning definition of the index and special cases are given.