Critical second order operators on time scales

Pages: 653 - 659, Issue Special, September 2011

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Petr Hasil - Department of Mathematics, Mendel University in Brno, Zemědělská 1, CZ-61300 Brno, Czech Republic (email)
Petr Zemánek - Department of Mathematics and Statistics, Falculty of Science Masaryk University, Kotlářská 2, CZ-61137 Brno, Czech Republic (email)

Abstract: 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

Received: June 2010;      Revised: March 2011;      Published: October 2011.