Volume 19, Issue 1

Abstract. We give a meaning to the nonlinear characteristic Cauchy problem for the wave equation in base form by replacing it by a family of non-characteristic ones. This leads to a well-formulated problem in an appropriate algebra of generalized functions. We prove existence of a solution and we precise how it depends on the choice made. We also check that in the classical case (non-characteristic) our new solution coincides with the classical one.

Abstract. In this paper, we investigate some Riesz space (vector lattice) properties of the space of real statistically convergent sequences. We prove that this space is an order dense Riesz subspace of the linear space of all real sequences, but it is not an ideal.

Abstract. In this work we are interested in the existence of solutions for the Dirichlet problem associated with the degenerate nonlinear elliptic equations in the setting of the weighted Sobolev spaces .

Abstract. In the paper we present sufficient conditions for property (B) and the oscillation of the third-order nonlinear functional differential equation with mixed arguments where . We deduce properties of the studied equations by establishing new comparison theorems so that property (B) and the oscillation are resulted from the oscillation of suitable first order equations.

Abstract. In this paper we present some properties of -upper continuous functions. We give a condition equivalent to -upper continuity and find maximal additive and maximal multiplicative classes for the family of -upper continuous functions. These classes depend on whether or . To describe maximal additive and maximal multiplicative classes for 1-upper continuous function, we need the notions of sparsity and topology.

Abstract. In this paper we prove the existence of metastable solutions to a general thermodynamically consistent mass-conserving Becker–Döring model which incorporates an inert substance. We make use of the methods for the standard model discussed by Penrose in 1989. We include an efficient numerical algorithm for approximating the thermodynamically consistent models.

Abstract. We examine the stochastic parabolic integral equation of convolution type where takes values in with a σ-finite measure space, and . The linear operator A maps into , is nonnegative and admits a bounded H ∞ -calculus on . The kernels are powers of t , with , , and , . We show that, in the maximal regularity case, where , one has the estimate where c is independent of G . Here and denotes fractional integration if , and fractional differentiation if , both with respect to the t -variable. The proof relies on recent work on stochastic differential equations by van Neerven, Veraar and Weis, and extends their maximal regularity result to the integral equation case.

Abstract. Best possible upper and lower bounds are given for the logarithmic and identric mean values in terms of the generalized centroidal mean.

Abstract. Many authors studied families of complex valued functions, which are holomorphic in bounded complete n -circular domains and fulfil some geometric conditions. The above functions were applied later to research families of locally biholomorphic mappings in ℂ n . In this paper we consider a problem of inclusions between a few of such families and families , , which are defined by applying a function decomposition with respect to the group of k th roots of unity.