Critical second order operators on time scales

Petr Hasil; Petr Zemánek

doi:10.3934/proc.2011.2011.653

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2011, Volume 2011: 653-659. Doi: 10.3934/proc.2011.2011.653 open access

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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
2.
Department of Mathematics and Statistics, Falculty of Science Masaryk University, Kotlářská 2, CZ-61137 Brno

Received: May 31, 2010

Revised: February 28, 2011

Published: August 2017

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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.

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