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These results are shown to be advantageous in studying the behavior at infinity of a class of unboundedly perturbed continuous and discontinuous time-varying systems that is frequently encountered in Lyapunov theory. In particular, sufficient conditions are given to ensure the positivity, the asymptotic stability and the instability of solutions of unidimensional and multidimensional systems. To illustrate the proposed results, several examples are simulated.<\/jats:p>","DOI":"10.1093\/imamci\/dnab039","type":"journal-article","created":{"date-parts":[[2021,11,17]],"date-time":"2021-11-17T04:23:13Z","timestamp":1637122993000},"page":"60-79","source":"Crossref","is-referenced-by-count":2,"title":["Behavior near time infinity of solutions of nonautonomous systems with unbounded perturbations"],"prefix":"10.1093","volume":"39","author":[{"given":"M F M","family":"Naser","sequence":"first","affiliation":[{"name":"Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan"}]}],"member":"286","published-online":{"date-parts":[[2021,12,9]]},"reference":[{"key":"2022030217385949400_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/b139028","volume-title":"Liapunov Functions and Stability in Control Theory","author":"Bacciotti","year":"2005"},{"key":"2022030217385949400_ref2","doi-asserted-by":"crossref","DOI":"10.1155\/2014\/395089","article-title":"A Generalized Solow\u2013Swan Model","volume":"2014","author":"Cai","year":"2014","journal-title":"Abstract Appl. 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