In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an IVP of first order hybrid  random differential equations with the linear perturbation of second type. A comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential eq...

The complexity of computing the Galois group of a linear differential equation is of general interest. In a recent work, Feng gave the first degree bound on Hrushovski’s algorithm for computing the Galois group of a linear differential equation. This bound is the degree bound of the polynomials used in the first step of the algorithm for finding a proto-Galois group (see Definition 2.8) and is ...

In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

In this paper we consider design of observers for non-linear models containing both dynamic and algebraic equations, so called differential-algebraic equations (DAE) or descriptor models. The observer is formulated as a DAE and the main results of the paper include conditions that ensure local stability of the observer and also that the observer has index 1. Design methodology is presented and ...

Tension-Leg Platform (TLP) is a vertically moored floating structure. The platform is permanently mooredby tendons. Surge equation of motion of TLP is highly nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. This paper compare the dynamic motion responses of a TLP in regular sea waves obtained by applying three method in time domain usin...

If solutions of a non-linear differential equation are contained in solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say tha...

This paper deals with state estimation of micro tunable capacitor subjected to nonlinear electrostatic force. For this end a nonlinear observer has been designed for state estimation of the structure.  Necessary and sufficient conditions for construction of the observer are presented. Stability of the observer is checked using Lyapunov theorem. Observer design is based on converting of differen...

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the fo...