English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study a semilinear differential-algebraic equation (DAE) with the focus onthe Lagrange stability (instability). The conditions for the existence anduniqueness of global solutions (a solution exists on an infinite interval) ofthe Cauchy problem, as well as conditions of the boundedness of the globalsolutions, are obtained. Furthermore, the obtained conditions for the Lagrangestability of the semilinear DAE guarantee that every its solution is global andbounded, and, in contrast to theorems on the Lyapunov stability, allow to provethe existence and uniqueness of global solutions regardless of the presence andthe number of equilibrium points. We also obtain the conditions of theexistence and uniqueness of solutions with a finite escape time (a solutionexists on a finite interval and is unbounded, i.e., is Lagrange unstable) forthe Cauchy problem. We do not use constraints of a global Lipschitz conditiontype, that allows to use the work results efficiently in practicalapplications. The mathematical model of a radio engineering filter withnonlinear elements is studied as an application. The numerical analysis of themodel verifies the results of theoretical investigations.

Lagrange stability of semilinear differential-algebraic equations and application to nonlinear electrical circuits