id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-435	Meng, Fengjuan; Zhang, Fubao; Zhang, Yuanyuan	Multiple positive solutions for biharmonic equation of Kirchhoff type involving concave-convex nonlinearities	2020	15	.pdf	application/pdf	6434	361	80	Note that 〈I ′λ(un), un〉=0 and 〈I ′λ(un), un〉 − 〈I ′λ(u), u〉 = 〈I ′λ(un)− I ′λ(u), u〉 − 〈I ′λ(un), un − u〉 → 0, as n→∞, (2.12) we have 〈I ′λ(u), u〉 = 0, which implies u ∈ Nλ. = 〈I ′λ(un)− I ′λ(u), un − u〉 = ‖un − u‖2 + b ∫ RN |∇un|2dx ∫ RN |∇(un − u)|2dx − b (∫ RN |∇u|2dx− ∫ RN |∇un|2dx )∫ RN ∇u∇(un − u)dx − λ ∫ RN f1(x)(|un|q−2un − |u|q−2u)(un − u)dx − ∫ RN f2(x)(|un|p−2un − |u|p−2u)(un − u)dx = ‖un − u‖2 + b ∫ RN |∇un|2dx ∫ RN |∇(un − u)|2dx+ o(1)	cache/ejde-435.pdf	txt/ejde-435.txt