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A dynamical system in a Hilbert space with a weakly attractive nonstationary point

Ivo Vrkoč (1993)

Mathematica Bohemica

A differential equation is a Hilbert space with all solutions bounded but with so finite nontrivial invariant measure is constructed. In fact, it is shown that all solutions to this equation converge weakly to the origin, nonetheless, there is no stationary point. Moreover, so solution has a non-empty Ω -set.

Decoupling normalizing transformations and local stabilization of nonlinear systems

S. Nikitin (1996)

Mathematica Bohemica

The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given.

Existence and stability of solutions for semilinear Dirichlet problems

Marek Galewski (2006)

Annales Polonici Mathematici

We provide existence and stability results for semilinear Dirichlet problems with nonlinearities satisfying some general local growth conditions. We derive a general abstract result which we then apply to prove the existence of solutions, their stability and continuous dependence on parameters for a sixth order ODE with Dirichlet type boundary data.

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