Hartman-Wintner type lemma, oscillation, and conjugacy criteria for half-linear difference equations

0359570 - MÚ 2012 US eng J - Journal Article
Řehák, Pavel
Hartman-Wintner type lemma, oscillation, and conjugacy criteria for half-linear difference equations.
Journal of Mathematical Analysis and Applications. Roč. 252, č. 2 (2000), s. 813-827. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR GA201/99/0295
Institutional research plan: CEZ:AV0Z1019905
Keywords : half-linear difference equation * Riccati technique * Hartman-Wintner lemma * discrete oscillation
Subject RIV: BA - General Mathematics
Impact factor: 0.431, year: 2000

We discuss oscillatory properties of the second order half-linear difference equation Delta (r(k)/Deltay(k)/(alpha -2)Deltay(k)) + p(k)/y(k+1)/(alpha -2)y(k+1) = 0, where alpha > 1. In particular, we establish the discrete half-linear extension of the Hartman-Wintner lemma and oscillatory and conjugacy criteria as an application of this lemma. The proofs of all these results and also of most of the other statements in this paper are based on the Riccati technique. (C) 2000 Academic Press.
Permanent Link: http://hdl.handle.net/11104/0197336