id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-222	Schechter, Martin	Infinite dimensional extensions of the Landesman-Lazer theorem	2021	12	.pdf	application/pdf	4408	265	85	→ −∞ as ‖v‖ → ∞, v ∈ N ′. For w ∈ M we write w = w0 + w′, where w0 ∈ N(A) and w′ ∈M ′. Since |F (x,w)− F (x,w0)| ≤ V (x)|w′| we have G(w) ≥ Let f(x, t) be a Caratheódory function on Ω× R such that (D) |f(x, t)| ≤ V (x) ∈ L2(Ω), x ∈ Ω, t ∈ R, (E) f(x, t)→ f±(x) a.e. as t→ ±∞, 216 M. SCHECHTER EJDE/SI/01 (F) either sup v∈N(A) ∫ Ω F (x, v)dx <∞ (2.1) or inf v∈N(A) ∫ Ω F (x, v)dx > −∞, (2.2) where F (x, t) :	cache/ejde-222.pdf	txt/ejde-222.txt