We present several results on exact controllability for linear and nonlinear parabolic equations, both when the distributed control is acting linearly or nonlinearly on the whole domain. As a very particular case, we extend some recent works by means of a simpler constructive approach....

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

This paper presents simulation results on the robustness of normal parametric inference in non-linear mixed models. A linearization approach to inference is compared with two two-stage methods (standard two-stage, STS, and global two-stage, GTS). When the assumptions of normality of the...

This study investigates the impact of uncertainty shocks on macroeconomic activity in Korea. For this purpose, a Smooth Transition VAR model is employed to document the state-dependent dynamics of two distinct types of uncertainty shocks, namely, financial market based and news-based. When...

We have studied a series of (ansätze) ordinary differential equations of the first-order, which correspond to the travelling (and/or solitary) wave solutions of some nonlinear partial differential equations. We have investigated the conditions, under which the nonlinear partial differential...

Using the path-integral formalism we develop an accurate and easy-to-compute semi-analytical approximation to transition probabilities and Arrow-Debreu densities for arbitrary diffusions. We illustrate the accuracy of the method by presenting results for the Black-Karasinski model for which the...

A principal distinction of neural network based methods of approximation from conventional methods is a hidden inside algorithmic function, which is defined by the neural network topology and is enough sophisticated to make appropriate fitting process. There is a new construction named...

We study a symmetric nonlinear eigenvalue problem arising in earthquake initiation and we establish the existence of infinitely many solutions. Under the effect of an arbitrary perturbation, we prove that the number of solutions becomes greater and greater if the perturbation tends to zero with...