Peculiarities in power type comparison results for half-linear dynamic equations

0389740 - MÚ 2013 RIV US eng J - Journal Article
Řehák, Pavel
Peculiarities in power type comparison results for half-linear dynamic equations.
Rocky Mountain Journal of Mathematics. Roč. 42, č. 6 (2012), s. 1995-2013. ISSN 0035-7596. E-ISSN 1945-3795
R&D Projects: GA AV ČR KJB100190701
Institutional support: RVO:67985840
Keywords : half-linear dynamic equation * time scale * comparison theorem
Subject RIV: BA - General Mathematics
Impact factor: 0.389, year: 2012
http://projecteuclid.org/euclid.rmjm/1361800616

We look for conditions guaranteeing that oscillatory properties of a half-linear dynamic equation are preserved when the power in the nonlinearities is changed. In particular, we discuss discrepancies (which indeed occur) between the results on different time scales. We provide an example showing an optimality of one of the assumptions. We also present one generalization of a standard Sturm-Picone type comparison theorem and give an important note on the smoothness condition for the coefficient in the leading term which concerns general theory of second order dynamic equations. Many of our observations are new also in the differential and difference equations cases.
Permanent Link: http://hdl.handle.net/11104/0218677