We introduce mountain-pass type arguments in the context of orbital instability for Klein-Gordon equations. Our aim is to illustrate on two examples how these arguments can be useful to simplify proofs and derive new results of orbital stability/instability. For a power-type nonlinearity, we prove that the ground states of the associated stationary equation are minimizers of the functional acti...

A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant ‘hyperbolic’ models such as minisuperspace quantum cosmology. The connection with sumover-histories constructions is exhibited and the physical equivalence or inequivalence of different such schemes is analyzed. The discussion focuses on comparing construction...

A spatially discrete version of the general kink-bearing nonlinear Klein-Gordon model in (1 + 1) dimensions is constructed which preserves the topological lower bound on kink energy. It is proved that, provided the lattice spacing h is suuciently small, there exist static kink solutions attaining this lower bound centred anywhere relative to the spatial lattice. Hence there is no Peierls-Nabarr...

A spatially discrete version of the general kink-bearing nonlinear Klein-Gordon model in (1 + 1) dimensions is constructed which preserves the topological lower bound on kink energy. It is proved that, provided the lattice spacing h is sufficiently small, there exist static kink solutions attaining this lower bound centred anywhere relative to the spatial lattice. Hence there is no Peierls-Naba...

We study a system of nonlinear Klein-Gordon equations with viscoelastic and degenerate damping in bounded domain. prove the global existence exponential growth solutions negative initial energy.