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

Critical second order operators on time scales

Petr Hasil 1, and  Petr Zemánek 2,

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.
Keywords: Time scales; second order operator; critical operator; recessive solution; dominant solution; one term operator..
Mathematics Subject Classification: Primary: 34C99,39A12; Secondary: 47B36.
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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