id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1514	Alvarez-Caudevilla, Pablo; Brandle, Cristina; Sonowal, Devashish	Positive solutions for n-dimensional fourth-order systems under a parametric condition	2025	10	.pdf	application/pdf	5150	229	74	On the other hand, we have that due to f∞ > 1, there exists ε ∈ (0, 1) and k > 0, so that f1(x, u1, u2) + f2(x, u1, u2) ≥ (1 + ε)(L1u1 + L2u2), (4.6) for all x ∈ Ω and u1, u2 ≥ 0, u1 + u2 ≥ k. Since 1 < f0, there exists ε ∈ (0, 1) and R0 > 0, small, so that f1(x, u1, u2) + f2(x, u1, u2) ≥ (1 + ε)(L1u1 + L2u2), EJDE-2025/56 N-DIMENSIONAL FOURTH-ORDER SYSTEMS 9 for all x ∈ Ω and u1, u2 ≥ 0, u1+u2 ≤ R0.	cache/ejde-1514.pdf	txt/ejde-1514.txt