id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-130	Hasil, Petr; Sisolakova, Jirina; Vesely, Michal	Oscillation of modified Euler type half-linear differential equations via averaging technique	2022	16	.pdf	application/pdf	6933	437	78	= 0, (3.1) lim t→∞ f(t)g2(t) t log t = 0, (3.2) lim t→∞ f(t)g(t) t = 0, (3.3) ginf := lim inf t→∞ g(t) > 0. (3.4) Especially, (3.2) and (3.4) give lim t→∞ f(t)g(t) t log t = 0, (3.5) 6 P. HASIL, J. ŠIŠOLÁKOVÁ, M. VESELÝ EJDE-2022/41 i.e., lim t→∞ t log t f(t)g(t) =∞. (3.6) − 1 f(t) ∫ t+f(t) t r(τ)| cosp ϕ(τ)|p dτ ∣∣∣ ≤ lim sup t→∞ 1 f(t) ∫ t+f(t) t r(τ) ∣∣ |cosp (ave[ϕ, f ](t))|p − | cosp ϕ(τ)|p ∣∣dτ ≤ lim sup t→∞ 1 f(t) ∫ t+f(t) t r(τ)C |ave[ϕ, f ](t)− ϕ(τ)|dτ ≤ lim sup t→∞ C ( t log t f(t)g(t) max τ∈[t,t+f(t)] |ϕ(τ)− ave[ϕ, f ](t)| ) × f(t)g2(t) t log t · 1 f(t)g(t) ∫ t+f(t) t r(τ) dτ = lim sup t→∞ C ·∆ (ϕ, ave[ϕ, f ]) · f(t)g2(t) t log t · r[f, g], i.e., lim t→∞ ∣∣∣ |cosp (ave[ϕ, f ](t))|p ave[r, f ](t)	cache/ejde-130.pdf	txt/ejde-130.txt