id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
american_scientific_journal-1155	Valdes, Juan E. Nápoles; Bittencurt, Luciano M. Lugo Motta	A Note on Bounded Solutions of a Generalized Lienard Type System	2016	6	.pdf	application/pdf	1752	116	68	= 𝑐𝑐𝑡𝑡𝑠𝑠. Integrating the first equation of the system (1.1), we get: 𝑥𝑥(𝑡𝑡) = 𝑥𝑥(𝑇𝑇 − 𝛿𝛿) + � 𝛼𝛼(𝑠𝑠)𝑑𝑑𝑠𝑠 𝑡𝑡 𝑇𝑇−𝛿𝛿 − � 𝛽𝛽�𝑦𝑦(𝑠𝑠)�𝐹𝐹�𝑥𝑥(𝑠𝑠)�𝑑𝑑𝑠𝑠 𝑡𝑡 𝑇𝑇−𝛿𝛿 , with ∫ 𝛼𝛼(𝑠𝑠)𝑑𝑑𝑠𝑠𝑡𝑡 𝑇𝑇−𝛿𝛿 ≤ 𝑐𝑐, (𝑐𝑐 = 𝑐𝑐𝑡𝑡𝑠𝑠) because 𝑦𝑦 is bounded. Integrating the last inequality, we have: (𝑥𝑥´(𝑡𝑡0) + 𝛽𝛽�𝑦𝑦(𝑡𝑡0)�𝐹𝐹�𝑥𝑥(𝑡𝑡0)�(𝑡𝑡 − 𝑡𝑡0) ≤ 𝑥𝑥(𝑡𝑡) − 𝑥𝑥(𝑡𝑡0) then, we conclude (𝑥𝑥´(𝑡𝑡0) + 𝛽𝛽�𝑦𝑦(𝑡𝑡0)�𝐹𝐹�𝑥𝑥(𝑡𝑡0)�(𝑡𝑡 − 𝑡𝑡0) + 𝑥𝑥(𝑡𝑡0)	cache/american_scientific_journal-1155.pdf	txt/american_scientific_journal-1155.txt