A geometric approach to invariant sets for dynamical systems.
A topological structure of solution sets to evolution systems
Approximation structures and applications to evolution equations.
Blow-up of solutions to a periodic nonlinear dispersive rod equation.
Center manifold and exponentially-bounded solutions of a forced Newtonian system with dissipation.
Chaos and shadowing around a homoclinic tube.
Continuation of the connection matrix for singularly perturbed hyperbolic equations
Differentiable semiflows for differential equations with state-dependent delays.
Existence and approximation results for gradient flows
This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Existence of doubly-weighted pseudo almost periodic solutions to non-autonomous differential equations.
Finite dimensional dynamics for Kolmogorov-Petrovsky-Piskunov equation.
Generation of analytic semi-groups in L2 for a class of second order degenerate elliptic operators
Gradient systems of closed operators
A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.
Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach
In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing.
Numerical Approximations of the Dynamical System Generated by Burgers’ Equation with Neumann–Dirichlet Boundary Conditions
Using Burgers’ equation with mixed Neumann–Dirichlet boundary conditions, we highlight a problem that can arise in the numerical approximation of nonlinear dynamical systems on computers with a finite precision floating point number system. We describe the dynamical system generated by Burgers’ equation with mixed boundary conditions, summarize some of its properties and analyze the equilibrium states for finite dimensional dynamical systems that are generated by numerical approximations of this...
Periodic point, endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces.
Periodic solutions of certain third order differential systems with nonlinear dissipation
Periodic solutions of dissipative dynamical systems with singular potential and p-Laplacian
By using the topological degree theory and some analytic methods, we consider the periodic boundary value problem for the singular dissipative dynamical systems with p-Laplacian: , x(0) = x(T), x’(0) = x’(T). Sufficient conditions to guarantee the existence of solutions are obtained under no restriction on the damping forces d/dt gradF(x).
Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach
A translation along trajectories approach together with averaging procedure and topological degree are used to derive effective criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations. It is shown that a topologically nontrivial zero of the averaged right hand side is a source of periodic solutions for the equations with increased frequencies. Our setting involves equations on closed convex cones, therefore it enables us to study positive solutions...
Semilinear Cauchy Problems with Almost Sectorial Operators
Existence of a mild solution to a semilinear Cauchy problem with an almost sectorial operator is studied. Under additional regularity assumptions on the nonlinearity and initial data we also prove the existence of a classical solution to this problem. An example of a parabolic problem in Hölder spaces illustrates the abstract result.