id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-666	Bandyopadhyay, Shalmali; Lewis, Thomas; Mavinga, Nsoki	Existence of maximal and minimal weak solutions and finite difference approximations for elliptic systems with nonlinear boundary conditions	2025	21	.pdf	application/pdf	10506	571	77	∈ ∂Ω. Throughout this article we assume that each fi satisfies the quasimonotonicity condition (A1) the functions fi are quasimonotone nondecreasing in the sense that f1(x, u1, u2) is nonde- creasing in u2 for all fixed x ∈ ∂Ω, u1 ∈ R, and f2(x, u1, u2) is nondecreasing in u1 for all fixed x ∈ ∂Ω, u2 ∈ R. In this article, we establish the existence of maximal and minimal weak solutions for (1.1). We define the map T : J → (H1(Ω))2 by T (U) =W , where J := {U = (u1, u2) ∈ (H1(Ω))2 : U ≤ U ≤ U} and W = (w1, w2) is the unique weak solution of the decoupled system −∆wi + wi = 0 in Ω; ∂wi ∂η + kwi = fi(x, u1, u2) + kui on ∂Ω, i = 1, 2, (2.1) where k = k1 + k2 ≥ 0.	cache/ejde-666.pdf	txt/ejde-666.txt