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 index in Hilbert spaces and a problem of Angenent and van der Vorst
In a recent paper [9] we presented a Galerkin-type Conley index theory for certain classes of infinite-dimensional ODEs without the uniqueness property of the Cauchy problem. In this paper we show how to apply this theory to strongly indefinite elliptic systems. More specifically, we study the elliptic system in Ω, in Ω, u = 0, v = 0 in ∂Ω, (A1) on a smooth bounded domain Ω in for "-"-type Hamiltonians H of class C² satisfying subcritical growth assumptions on their first order derivatives....
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.
Connected branches of asymptotically equivalent solutions to non-linear eigenvalue problems
We prove an existence theorem for connected branches of solutions to nonlinear operator equations in Banach spaces. This abstract result is applied to the asymptotically equivalent solutions to nonlinear ordinary differential equations.
Connecting fast-slow systems and Conley index theory via transversality.
Connection between asymptotic properties and zeros of solutions of
Connections between Morse sets for delay-differential equations.
Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas....
Consensus of a two-agent system with nonlinear dynamics and time-varying delay
To explore the impacts of time delay on nonlinear dynamics of consensus models, we incorporate time-varying delay into a two-agent system to study its long-time behaviors. By the classical 3/2 stability theory, we establish a sufficient condition for the system to experience unconditional consensus. Numerical examples show the effectiveness of the proposed protocols and present possible Hopf bifurcations when the time delay changes.
Consequences of the meromorphic equivalence of standard matrix differential equations.
In this article we investigate the question [of] how meromorphic differential equations can be simplified by meromorphic equivalence. In the case of equations of block size 1, which generalizes the case of distinct eigenvalues, we identify a class of equations which are simplest possible in the sense that they carry the smallest number of parameters whithin their equivalence classes. We also discuss conditions under which individual equations can be simplified. Particular attention is paid to the...
Constant invariant solutions of the Poincaré center-focus problem.
Constants in the oscillation theory of higher order Sturm-Liouville differential equations.
Constrained least squares methods for linear timevarying DAE systems.
Constructing soliton and kink solutions of PDE models in transport and biology.
Constructing the minimal differential relation with prescribed solutions
Construction of a smooth Lyapunov function for an asymptotically stable set
Construction of interval wavelet based on restricted variational principle and its application for solving differential equations.
Construction of Lyapunov functionals for linear Volterra integrodifferential equations and stability of delay systems.
Construction of non-constant lower and upper functions for impulsive periodic problems.