id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1242	Feng, Meiqiang; Lu, Yichen	Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations	2025	16	.pdf	application/pdf	8094	500	81	Uniqueness of nontrivial solutions In this section, we use the following assumptions on f : (A1) f(x, u) Carathéodory conditions for x ∈ Ω and −∞ < u < +∞), and for fixed x ∈ Ω, f(x, u) is a decreasing function, that is f(x, u1) In this section, we suppose that f satisfies the following assumptions: (A3) f(x, u) satisfies Carathéodory conditions for x ∈ Ω and −∞ < u < +∞), and there exists 0 < σ ≤ N+4 N−4 such that |f(x, u)| ≤ a+ b|u|σ, a > 0, b > 0; (4.4) (A4) There exist 0 ≤ ξ < 1 2 and L > 0 such that F (x, u) = ∫ u 0 f(x, v)dv ≤ ξuf(x, u), ∀|u| ≥ L, x ∈ Ω; (4.5) (A5)	cache/ejde-1242.pdf	txt/ejde-1242.txt