Journal of Inequalities and Applications
Volume 4 (1999), Issue 4, Pages 345-373

Landau-type inequalities and LP-bounded solutions of neutral delay systems

Hans Günzler

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.


In Section 1 relations between various forms of Landau inequalities y(m)nλynmy(n)m and Halperin–Pitt inequalities y(m)εy(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.