In this paper we show that a function defined on a subset of a finite domain and which represents the restiction of an asymmetric and transitive binary relation on the subset can be extended to a utility function on the entire domain. A simple proof of Szpilrajn's Extension Theorem which is...

The problem is considered as to whether a monotone function defined on a subset of Euclidean space can be strictly monotonically extended to . It is proved that this is the case if and only if the function is Explicit formulas are given for a class of extensions which involves an arbitrary...

In this paper we study the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions in Banach spaces.We derive conditions under which the integral solutions exit

In this paper we establish asymptotic (biasymptotic) equivalence between spaces of solutions of a given linear homogeneous system and a perturbed system. The perturbations are of either linear or weakly linear characters. Existence of a homeomorphism between subspaces of almost periodic and...

We consider the method of quasi-reversibility for numerical solving of boundary-value problems for differential equations. A specific feature of our approach is the well-posedness of the problems we study. We illustrate the main idea of the method with several examples of typical problems of...

We study Gevrey properties and multisummability of power series in more than two variables that are formal solutions of a Cauchy problem for linear partial differential equations with constant coefficients. We extend earlier results in an article of Werner Balser, who has considered linear...

A kind of stochastic differential equations with jumps are offered first, then the Euler scheme for these equations are present, at last their continuous dependence on initial value and convergence are be studied