Based on [4], we prove a variation of the theorem in title, for equations with periodic coefficients, in Fréchet spaces. The main result gives equivalent conditions ensuring the reduction of such an equation to one with constant coefficient. In the particular case of C ∞ , we obtain the exact analogue of the classical theorem. Our approach essentially uses the fact that a Fréchet space is the l...

We give a short proof of a formula of Poincaré-Bertrand in the setting of time-harmonic solutions of the relativistic Dirac equation on a piecewise Liapunov surface, as well as for some versions of quaternionic analysis.

We present an equivariant Liapunov stability criterion for dynamical systems with symmetry. This result yields a simple proof of the energy–momentum–Casimir stability analysis of relative equilibria of equivariant Hamiltonian systems.

Physics of Fluids 11(1999), 875-879. In this paper, we discuss zonally periodic steady quasigeostrophic waves in a β−plane channel, by using variational methods. A class of steady quasigeostrophic waves are determined by the potential vorticity field profile, g(·), which is a function of the stream function. We show that zonally periodic steady quasigeostrophic waves exist when the bottom topog...

In this paper, we first compute the multiple non-trivial solutions of the Schrödinger equation on a square, by using the Liapunov-Schmidt reduction and symmetry-breaking bifurcation theory, combinedwith Legendre pseudospectralmethods. Then, starting from the non-trivial solution branches of the corresponding nonlinear problem, we further obtain the whole positive solution branch with D4 symmetr...

We construct the most general form of axially symmetric SU (2)-Yang-Mills fields in Bianchi cosmologies. The dynamical evolution of axially symmetric YM fields in Bianchi I model is compared with the dynamical evolution of the electromagnetic field in Bianchi I and the fully isotropic YM field in Friedmann-Robertson-Walker cosmolo-gies. The stochastic properties of axially symmetric Bianchi I-E...

We introduce a class of difference/differential equations which is sufficiently large to include systems of interest for applications, but at the same time sufficiently easy to handle. In this framework, we give in particular a detailed and rather complete study of the asymptotic behavior of pairs of oscillators. We finally introduce appropriate notions of stability and extend Liapunov first an...