A global existence and uniqueness result for a stochastic Allen–Cahn equation with constraint

This paper addresses the analysis of a time noise‐driven Allen–Cahn equation modelling the evolution of damage in continuum media in the presence of stochastic dynamics. The nonlinear character of the equation is mainly due to a multivoque maximal monotone operator representing a constraint on the damage variable, which is forced to take physically admissible values. By a Yosida approximation and a time‐discretization procedure, we prove a result of global‐in‐time existence and uniqueness of the solution to the stochastic problem. Copyright © 2017 John Wiley & Sons, Ltd.     

A general existence theorem for symmetric floating drops

An existence theorem for floating drops due to Elcrat, Neel, and Siegel is generalized. The theorem applies to all radially symmetric domains, and to both light and heavy floating drops, and utilizes new results in annular capillary theory.     

Existence theorem for a stochastic wave equation with discontinuous unbounded coefficients

We prove an existence theorem for stochastic hyperbolic equations with measurable locally bounded coefficients. A solution of a stochastic hyperbolic equation is understood as a martingale solution of the stochastic inclusion corresponding to the equation.     

A global existence theorem for the four-body problem of Newtonian mechanics

It is shown that for the planar or three-dimensional two-, three-, or four-body problems of celestial mechanics, almost all initial conditions (in the sense of Lebesgue measure and Baire category) lead to solutions which exist for all time.     

A general Choquet–Deny theorem for nilpotent groups

Let G be a locally compact second countable nilpotent group. Let μ be a probability measure on the Borel sets of G. We prove that any bounded continuous function h on G solution of the convolution equation

verifies h(gx)=h(g) for all (g,x)G×suppμ.     

Reversible coagulation–fragmentation processes and random combinatorial structures: Asymptotics for the number of groups

The equilibrium distribution of a reversible coagulation‐fragmentation process (CFP) and the joint distribution of components of a random combinatorial structure (RCS) are given by the same probability measure on the set of partitions. We establish a central limit theorem for the number of groups (= components) in the case a(k) = qk^p?1, k ≥ 1, q, p > 0, where a(k), k ≥ 1, is the parameter function that induces the invariant measure. The result obtained is compared with the ones for logarithmic RCS's and for RCS's, corresponding to the case p < 0. © 2004 Wiley Periodicals, Inc. Random Struct. Alg. 2004     

An existence result for a semilinear equation in some domains with unbounded boundary

In this paper we prove the existence of at least one positive solution of the equation

A lifting theorem for unbounded quasinormal operators

Relationships between minimal normal extensions of spectral and cyclic type of an unbounded quasinormal operator are discussed and some properties such as, for example, tightness of such extensions are established. A Yoshino type criterion on the lifting of the strong commutant of an unbounded quasinormal operator is proved.     

A lifting theorem for subordinated invariant kernels

A lifting property for subordinated invariant kernels is proved and extended to operator-valued kernels. The connections with the classical Nagy-Foias lifting theorem and with Naimark's dilation theorem are indicated, as well as possible applications to scattering structures and quantum field theory.     

An existence theorem for a type of functional differential equation with infinite delay

Summary We prove an existence theorem for a functional differential equation with infinite delay using the Schauder fixpoint theorem. We extend a result in [19] applying the fixed point procedure in an appropriate function space.