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, by considering the Adomian decomposition method, explicit solutions are calculated for partial differential equations with initial conditions. The method does not need linearization, weak nonlinearly assumptions or perturbation theory. The decomposition series analytic solution of...

In this paper, by considering the Adomian decomposition method, explicit solutions are calculated for partial differential equations with initial conditions. The method does not need linearization, weak nonlinearly assumptions or perturbation theory. The decomposition series analytic solution of...

In this article we review and extend results on summability of formal solutions of Cauchy problems for linear partial differential equations, in two variables, with constant coefficients. Moreover, we show how one can use these results to find corresponding ones for solutions to inhomogeneous...

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