id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-380	Silva, Kaye; Moreno Sousa, Steffanio	Multiplicity of positive solutions for a gradient type cooperative/competitive elliptic system	2020	14	.pdf	application/pdf	6255	378	86	For λ, µ ∈ R and w ∈ X we introduce Hλ,µ(w) Moreover, ψλ,µ,w is decreasing; We start with the study of N+ λ,µ. Observe from Proposition 2.2 that if N+ λ,µ 6= ∅ then there exist (λ, µ) ∈ R2 and w ∈ X such that Hλ(w) < 0 or equivalently∫ |∇u|2 + ∫ |∇v|2 − µ ( ∫ |u|2 + ∫ |v|2 ) 2 ∫ uv < λ, therefore we are led to the study of the function λmin(µ;w) := ‖w‖2 − µ‖w‖22 2 ∫ uv , w ∈ X , ∫ uv > 0. (2.1)	cache/ejde-380.pdf	txt/ejde-380.txt