Abstract:
We study the Lyapunov inequalities for the time scales, for discrete linear
Hamiltonian systems on the time scales. We show the strong instability
and stability standing waves for nonlinear Klein – Gordon eqations and
Klein – Gordan- Zakharov system. We also show the stability and
instability of standing waves for one- dimensional nonlinear Schrodinger
equation with multiple – power nonlinearity and stability of bound states
of Hamiltonian partial differential equations in the degenerated cases.
The moment identities for Skorohod integrals, random Hermite
polynomials with Girsanov identities on the Wiener space are
characterized. The transfer principle method from Wiener to Poisson
space and measure invariance on the Lie- Wiener path space are
discussed. We show the Laplace transform identities and describe the
measure – preserving transformations on the Lie- Wiener – Poisson
spaces.
