We consider the typical behaviour of random dynamical systems order-preserving interval homeomorphisms with a positive Lyapunov exponent condition at endpoints. Our study removes any requirement for continuous differentiability save existence finite derivatives endpoints interval. construct suitable Baire space structure this class systems. Generically within our space, we show that stationary ...

We exhibit a dense set of limit periodic potentials for which the corresponding one-dimensional Schrödinger operator has a positive Lyapunov exponent for all energies and a spectrum of zero Lebesgue measure. No example with those properties was previously known, even in the larger class of ergodic potentials. We also conclude that the generic limit periodic potential has a spectrum of zero Lebe...

In this article, we study the steady generalized Navier-Stokes equations in a half-space in the setting of variable exponent spaces. We first establish variable exponent spaces of Clifford-valued functions in a half-space. Then, using this operator theory together with the contraction mapping principle, we obtain the existence and uniqueness of solutions to the stationary Navier-Stokes equation...

In this paper the weak fixed point property (w-FPP) and (FPP) in Variable Lebesgue Spaces are studied. Given (Ω,Σ,μ) a σ-finite measure p(⋅) variable exponent function, w-FPP is completely characterized for space Lp(⋅)(Ω) terms of function absence an isometric copy L1[0,1]. particular, every reflexive has FPP our results bring to light existence some nonreflexive spaces satisfying w-FPP, sharp ...

In the present note we investigate norm and almost everywhere convergence of the inverse continuous wavelet transform in the variable Lebesgue space. Mathematics Subject Classification (2010): Primary 42C40, Secondary 42C15, 42B08, 42A38, 46B15.

In this paper we are concerned with the study of a class of quasilinear elliptic differential inclusions involving the anisotropic − →p (·)-Laplace operator, on a bounded open subset of Rn which has a smooth boundary. The abstract framework required to study this kind of differential inclusions lies at the interface of three important branches in analysis: nonsmooth analysis, the variable expon...

It is well-known that a random variable, i.e. a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an extension of this to multivariate functions. This is motivated by some recent constructions of random