Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this paper, an asymptotic theory for a class of fourth-order differential equations is developed for a general class of four-order equations. But the theory is restricted to the case where the coefficients of the differential equation have different orders of magnitude for large x.
Abstract: An asymptotic theory is developed for a class of fourth-order differential equations. Under a general conditions on the coefficients of the differential equation we obtained the forms of the asymptotic solutions such that the solutions have different orders of magnitude for large x.
4 citations
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14 Apr 2011TL;DR: In this article, a simplified procedure for finding such expansions is presented for the relation (n+ 1)(16n − 15)qn+1 = (128n + 40n − 82n − 45) qn − n − n(256n − 240n + 64n − 7), qn−1 + (16n + 1)n(n − 1)/qn−2.
Abstract: Any solution of Eq. (1) can be extended in the real direction, but under the passage to a different domain, its asymptotics generally changes. A general procedure for finding such expansions is fairly complicated, but in most cases, a simplified procedure is sufficient; we describe its application for the example of the relation (n+ 1)(16n − 15)qn+1 = (128n + 40n − 82n − 45)qn − n(256n − 240n + 64n − 7)qn−1 + (16n + 1)n(n − 1)qn−2. (3)
4 citations
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TL;DR: In this article, the authors study a generalized asymptotic equivalence between the solutions of the difference equations, and show that the equivalence can be obtained by a generalized linear equivalence.
Abstract: The purpose of this paper is the study of a generalized asymptotic equivalence between the solutions of the difference equations
4 citations
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4 citations
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TL;DR: In this article, a sufficient condition is derived based on matrix inequality, in which the system is found to be impulse-free and asymptotic stable, and based on this result, the problem of stabilization is considered by using the Riccati equation corresponding to this Lyapunov equation.
Abstract: In this paper,the problem of asymptotic stability and the problem of stabilization for singular time-varying systems with time-delay are studied.First of all,a sufficient condition is derived based on matrix inequality,in which the system is found to be impulse-free and asymptotic stable.furthermore,based on this result,the problem of stabilization is considered by using the Riccati equation corresponding to this Lyapunov equation.Finally an example is given to illustrate the validity of the main results proposed.
4 citations