Lipschitz and darbo conditions for the superposition operator in some non-ideal spaces of smooth functions

Let X be a Banach space of differentiable functions and A: XX be a superposition operator. We consider for A the conditions

Sull'interpolazione di operatori nonlineari noncompatti in spazi di funzioni integrabili

Usando la misura di non compattezza di Hausdorff, si dimostra un teorema elementare di interpolazione per gli operatori nonlineari noncompatti tra retticoli di Banach di funzioni misurabili. Il teorema astratto viene illustrato tramite un'equazione integrale nonlineare del tipo di Hammerstein. An elementary interpolation theorem involving the Hausdorff measure of noncompactness for nonlinear operators in Banach lattices of measurable functions is proved. The abstract theorem is illustrated by a nonlinear noncompact integral operator equation of Hammerstein type.

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(Conferenza tenuta l'11 ottobre 1988)     

Straightforward and Scalable Synthesis of Diethyl Fluoro-(phenylsulfonyl)methylphosphonate

A process is described for the synthesis of diethyl fluoro(phenylsulfonyl)methylphosphonate which is easily and safely performed on a multi-kilogram scale.     

Analysis by the two-fluids model of the dynamical behavior of a viscoelastic fluid probed by dynamic light scattering

The dynamic properties of a model transient network have been studied by dynamic light scattering. The network is formed by microemulsion droplets linked by telechelic polymers (modified hydrophilic polymers with two grafted hydrophobic stickers). We compare the properties of two networks that are similar but for the residence time of the hydrophobic stickers in the droplets. The results are interpreted according to the so-called two-fluids model, which was initially developed for semidilute polymer solutions and which we extend here to any Maxwellian viscoelastic medium characterized by its elastic modulus and terminal time as measured by rheology. This model is found to describe consistently and quantitatively the experimental observations.     

Bifurcation points of Hammerstein equations

We apply global bifurcation theorems to systems of nonlinear integral equations of Hammerstein type involving a scalar parameter. To this end, we give sufficient conditions for the continuous dependence, compactness, Fréchet differentiability, and asymptotic linearity of the corresponding operators, which are more general than in the classical setting. These properties are ensured only after passing to some equivalent operator equation which typically contains fractional powers of the linear part. Finally, we show that the abstract hypotheses on the operators correspond to natural hypotheses on the kernel function and the nonlinearity in the Hammerstein equation under consideration.