id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-189	Costa, David G.	Remarks on compactness conditions and their application	2023	7	.pdf	application/pdf	3150	176	76	So, let us assume that J satisfies (i), (ii), but ‖un‖ → ∞ , and prove that c ∈ Γk. Therefore, using Holder’s inequality and Sobolev’s embedding as in (2.6), we obtain (with q ≥ 2N/(N + 2), N ≥ 3) | ∫ Ω g(un)u+ n dx| ≤ C( ∫ Ω |g(un(x))|q dx) 1 q ‖u+ n ‖ and, since g(un(x)) → 0 a.e. in Ω in view of (A4), an application of Lebesgue’s theorem once again implies the desired conclusion that c ∈ Γk in case (iii) holds.	cache/ejde-189.pdf	txt/ejde-189.txt