Nonuniqueness for the solutions of ordinary differential equations
Nonuniqueness of implicit lattice Nagumo equation
We consider the implicit discretization of Nagumo equation on finite lattices and show that its variational formulation corresponds in various parameter settings to convex, mountain-pass or saddle-point geometries. Consequently, we are able to derive conditions under which the implicit discretization yields multiple solutions. Interestingly, for certain parameters we show nonuniqueness for arbitrarily small discretization steps. Finally, we provide a simple example showing that the nonuniqueness...
Nonuniqueness results for ordinary differential equations
In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.
Nonuniqueness theorem for a singular Cauchy problem.
Nonuniqueness theorem for a singular Cauchy-Nicoletti problem.
Nonwandering points and the set of central motions in discontinuous disperse dynamic systems
Norm estimates for functions of two non-commuting matrices.
Normal and osculating planes of -regular curves.
Normal forms for certain singularities of vectorfields
normal forms are given for singularities of vectorfields on , which are not flat, and for vectorfields on with , the 1-jet of in the origin is a pure rotation, and some higher order jet of attracting or expanding.
Normal forms for singularities of one dimensional holomorphic vector fields.
Normal forms of analytic perturbations of quasihomogeneous vector fields: Rigidity, invariant analytic sets and exponentially small approximation
In this article, we study germs of holomorphic vector fields which are “higher order” perturbations of a quasihomogeneous vector field in a neighborhood of the origin of , fixed point of the vector fields. We define a “Diophantine condition” on the quasihomogeneous initial part which ensures that if such a perturbation of is formally conjugate to then it is also holomorphically conjugate to it. We study the normal form problem relatively to . We give a condition on that ensures that there...
Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part
We explore the convergence/divergence of the normal form for a singularity of a vector field on with nilpotent linear part. We show that a Gevrey- vector field with a nilpotent linear part can be reduced to a normal form of Gevrey- type with the use of a Gevrey- transformation. We also give a proof of the existence of an optimal order to stop the normal form procedure. If one stops the normal form procedure at this order, the remainder becomes exponentially small.
Normal modes of a lagrangian system constrained in a potential well
Normalisation des champs de vecteurs holomorphes
Normality of the maximum principle for absolutely continuous solutions to Bolza problems under state constraints
Normalization of Poincaré singularities via variation of constants.
We present a geometric proof of the Poincaré-Dulac Normalization Theorem for analytic vector fields with singularities of Poincaré type. Our approach allows us to relate the size of the convergence domain of the linearizing transformation to the geometry of the complex foliation associated to the vector field.
Norms of certain rational functions of a matrix and Schur's criterion for polynomials
Note on a discretization of a linear fractional differential equation
The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.
Note on a non-oscillation theorem of Atkinson.
Note on a paper of E. M. E. Zayed and S. F. M. Ibraham.