Stability of periodic solutions of state-dependent delay-differential equations

We consider a class of autonomous delay-differential equations

     

Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles

Consider in this paper a linear skew-product system

     

The local variational principle of topological pressure for sub-additive potentials

Let (X,T) be a topological dynamical system and be a sub-additive potential on C(X,R). Let U be an open cover of X. Then for any T-invariant measure μ, let . The topological pressure for open covers U is defined for sub-additive potentials. Then we have a variational principle:

     

Computations of critical groups and periodic solutions for asymptotically linear Hamiltonian systems

The purpose of this paper is two-fold. Firstly, we will give some parabolic-like conditions which improve the well-known angle conditions and allow further computations of the critical groups both at degenerate critical points and at infinity. As an application, we then consider the second-order Hamiltonian systems

     

Periodic points classify a family of Markov shifts

Ledrappier introduced the following type of space of doubly indexed sequences over a finite abelian group G,

     

On the support of solutions to the Ostrovsky equation with negative dispersion

In this article we prove that sufficiently smooth solutions of the Ostrovsky equation with negative dispersion:

     

Positive clustered layered solutions for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of RN:

     

On the support of solutions to the Zakharov-Kuznetsov equation

In this article we prove that sufficiently smooth solutions of the Zakharov-Kuznetsov equation:

     

Cauchy problem for the Ostrovsky equation in spaces of low regularity

In this article we consider the initial value problem for the Ostrovsky equation:

     

On the support of solutions to the Ostrovsky equation with positive dispersion

In this paper we prove that sufficiently smooth solutions of the Ostrovsky equation with positive dispersion,

     

Finite-dimensional attractors for the quasi-linear strongly-damped wave equation

We present a new method of investigating the so-called quasi-linear strongly-damped wave equations

     

On random perturbation of some intersective sets

Given a subset S of Z and a sequence I = (I_n)_n=1^∞ of intervals of increasing length contained in Z, let