Access the full text.
Sign up today, get DeepDyve free for 14 days.
O. Perron (1929)
Über Stabilität und asymptotisches Verhalten der Integrale von DifferentialgleichungssystemenMathematische Zeitschrift, 29
Differential Equations, Vol. 39, No. 10, 2003, pp. 1395–1403. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 10, 2003, pp. 1325–1333. Original Russian Text Copyright c 2003 by Kryzhevich, Pliss. ORDINARY DIFFERENTIAL EQUATIONS S. G. Kryzhevich and V. A. Pliss St. Petersburg State University, St. Petersburg, Russia Received February 17, 2003 The structural stability of systems of ordinary di erential equations with arbitrary dependence on time was studied in [1{4]. However, the existence of a homeomorphism taking the solutions of the nonperturbed system to the solutions of the perturbed system was not established there. Here we prove this fact under the assumptions stated in the cited papers. Consider the system of ordinary di erential equations x _ = X (t;x);x 2 R : (1) We assume that the vector X (t;x) and its Jacobi matrix @X (t;x)=@x with respect to x are uniformly continuous on the entire space R R and there exists a constant M> 0 such that jX (t;x)j M; j@X (t;x)=@xj M for all t 2 R and x 2 R .Here the symbol jj stands for the Euclidean norm of a vector or the corresponding matrix norm. Along with system (1), we consider the perturbed system
Differential Equations – Springer Journals
Published: Oct 11, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.