# American Institute of Mathematical Sciences

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2011, 2011(Special): 653-659. doi: 10.3934/proc.2011.2011.653

## Critical second order operators on time scales

 1 Department of Mathematics, Mendel University in Brno, Zemědělská 1, CZ-61300 Brno, Czech Republic 2 Department of Mathematics and Statistics, Falculty of Science Masaryk University, Kotlářská 2, CZ-61137 Brno, Czech Republic

Received  June 2010 Revised  March 2011 Published  October 2011

In this paper we introduce the concept of critical operators for dynamic operators of second order. Next, we show that an arbitrarily small (in a certain sense) negative perturbation of a non-negative critical operator leads to an operator which is no longer non-negative.
Citation: Petr Hasil, Petr Zemánek. Critical second order operators on time scales. Conference Publications, 2011, 2011 (Special) : 653-659. doi: 10.3934/proc.2011.2011.653
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