{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:00:33Z","timestamp":1760241633476,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T00:00:00Z","timestamp":1528416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004569","name":"Ministerstwo Nauki i Szkolnictwa Wyzszego","doi-asserted-by":"publisher","award":["04\/43\/DSPB\/0095"],"award-info":[{"award-number":["04\/43\/DSPB\/0095"]}],"id":[{"id":"10.13039\/501100004569","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We study asymptotic behavior of nonoscillatory solutions to second-order neutral difference equation of the form:    \u0394  (  r n  \u0394  (  x n  +  p n   x  n \u2212 \u03c4   )  )  =  a n  f  ( n ,  x n  )  +  b n  .    The obtained results are based on the discrete Bihari type lemma and a Stolz type lemma.<\/jats:p>","DOI":"10.3390\/sym10060207","type":"journal-article","created":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T11:19:31Z","timestamp":1528456771000},"page":"207","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Nonoscillatory Solutions to Second-Order Neutral Difference Equations"],"prefix":"10.3390","volume":"10","author":[{"given":"Ma\u0142gorzata","family":"Migda","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Pozna\u0144 University of Technology, Piotrowo 3A, 60-965 Pozna\u0144, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janusz","family":"Migda","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Pozna\u0144, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,8]]},"reference":[{"key":"ref_1","first-page":"77","article-title":"Almost oscillation criteria for second order neutral difference equation with quasidifferences","volume":"9","author":"Jankowski","year":"2014","journal-title":"Int. J. Differ. Equ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1016\/S0096-3003(02)00631-8","article-title":"Oscillation of second order nonlinear neutral delay difference equations","volume":"146","author":"Jiang","year":"2003","journal-title":"Appl. Math. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0096-3003(02)00286-2","article-title":"New oscillation criteria for second-order nonlinear neutral delay difference equations","volume":"142","author":"Saker","year":"2003","journal-title":"Appl. Math. 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