Journal of Inequalities and Applications
Volume 4 (1999), Issue 4, Pages 345-373
doi:10.1155/S1025583499000454
Landau-type inequalities and LP-bounded solutions of neutral delay systems
Mathematisches Seminar, Universität Kiel, Ludewig-Meyn-Str. 4, Kiel D 24098, Germany
Received 30 November 1998; Revised 21 January 1999
Copyright © 1999 Hans Günzler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In Section 1 relations between various forms of Landau inequalities ‖y(m)‖n≤λ‖y‖n−m‖y(n)‖m and Halperin–Pitt inequalities ‖y(m)‖≤ε‖y(n)‖+S(ε)‖y‖ are discussed, for arbitrary norms, intervals and Banach-space-valued y. In Section 2 such inequalities are derived for weighted LP-norms, Stepanoff- and Orlicz-norms.
With this, Esclangon–Landau theorems for solutions y of linear neutral delay difference-
differential systems are obtained: If y is bounded e.g. in a weighted LP- or Stepanoff-norm, then so are the y(m). This holds also for some nonlinear functional differential equations.