Landau-type inequalities and <inline-formula><graphic file="1029-242X-1999-749652-i1.gif"/></inline-formula>-bounded solutions of neutral delay systems

• Main Author: G&#252;nzler Hans
• Format: Article
• Language: English
• Published: SpringerOpen 1999-01-01
• Series: Journal of Inequalities and Applications
• Subjects: Landau inequalities; Esclangon&#8211;Landau theorem; <it>L</it>^P-bounded solutions; Neutral differential-difference systems
• Online Access: http://www.journalofinequalitiesandapplications.com/content/4/749652

<p/> <p>In Section 1 relations between various forms of Landau inequalities <inline-formula><graphic file="1029-242X-1999-749652-i2.gif"/></inline-formula> and Halperin&#8211;Pitt inequalities <inline-formula><graphic file="1029-242X-1999-749652-i3.gif"/></inline-formula> are discussed, for arbitrary norms, intervals and Banach-space-valued <inline-formula><graphic file="1029-242X-1999-749652-i4.gif"/></inline-formula>. In Section 2 such inequalities are derived for weighted <inline-formula><graphic file="1029-242X-1999-749652-i5.gif"/></inline-formula>-norms, Stepanoff- and Orlicz-norms.</p> <p>With this, Esclangon&#8211;Landau theorems for solutions y of linear neutral delay difference- differential systems are obtained: If <inline-formula><graphic file="1029-242X-1999-749652-i6.gif"/></inline-formula> is bounded e.g. in a weighted <inline-formula><graphic file="1029-242X-1999-749652-i7.gif"/></inline-formula>- or Stepanoff-norm, then so are the <inline-formula><graphic file="1029-242X-1999-749652-i8.gif"/></inline-formula>. This holds also for some nonlinear functional differential equations.</p>