Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 104043, 7 pages
doi:10.1155/2009/104043
Research Article

Bargmann-Type Inequality for Half-Linear Differential Operators

Gabriella Bognár1 and Ondřej Došlý2

1Department of Analysis, University of Miskolc, 3515 Miskolc-Egytemváros, Hungary
2Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

Received 7 May 2009; Revised 29 July 2009; Accepted 21 August 2009

Academic Editor: Martin J. Bohner

Copyright © 2009 Gabriella Bognár and Ondřej Došlý. 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

We consider the perturbed half-linear Euler differential equation (Φ(x′))′+[γ/tp+c(t)]Φ(x)=0, Φ(x):=|x|p−2x, p>1, with the subcritical coefficient γ<γp:=((p−1)/p)p. We establish a Bargmann-type necessary condition for the existence of a nontrivial solution of this equation with at least (n+1) zero points in (0,∞).