id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-463	Recova, Leandro; Rumbos, Adolfo	Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity	2020	15	.pdf	application/pdf	6461	313	73	The following limit holds lim |s|→+∞ 2F (x, s) s2 = +∞ uniformly for x ∈ Ω . s 0 |f(x, ξ)| dξ 6 a1s+ a1 p sp, EJDE-2020/60 SUPERLINEAR ELLIPTIC PROBLEM 5 for x ∈ Ω; so that, |F (x, s)| 6 a1 [ δ (s δ ) + δp p (s δ )p ] , for x ∈ Ω. (3.3) Consequently, since we are assuming that s > δ; so that s δ > 1, it follows from (3.3) that |F (x, s)| 6 a1 [ δ (s δ )p + δp p (s δ )p ] , for x ∈ Ω and s > δ, from which we obtain that |F (x, s)| 6 a1 δp (δ + δp) sp, for x ∈ Ω and s > δ, (3.4) where we have used the fact that p > 1, in view of that assumption p ∈ (2, 2∗) in (H1).	cache/ejde-463.pdf	txt/ejde-463.txt