id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-390	Papageorgiou, Nikolaos S.; Vetro, Calogero; Vetro, Francesca	Positive and nodal solutions for nonlinear nonhomogeneous parametric Neumann problems	2020	20	.pdf	application/pdf	8954	497	82	If ũλ 6= ûλ, then we can find z0 ∈ Ω such that ûλ(z0) < ũλ(z0) implies ûλ(z0) < ûλn(z0) for all n ≥ n0 (see (3.52)). By Proposition 3.2, we can find uθ ∈ Sθ ⊆ D+, u0 ∈ Sλ ⊆ D+ and uη ∈ Sη ⊆ D+ such that uθ − u0 ∈ int Ĉ+ and u0 − uη ∈ int Ĉ+, ⇒ u0 ∈ intC1(Ω)[uη, uθ].	cache/ejde-390.pdf	txt/ejde-390.txt