id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-123	Wang, Sainan; Su, Yu	Existence of solution to critical Kirchhoff-type equation with dipole-type potential	2022	18	.pdf	application/pdf	6574	489	89	Specifically, the Schrödinger equation for the wave function of an electron interacting with a polar molecule can be written as H = − ~ 2m ∆ + e x ·D |x|3 − E, where D is the dipole moment of the molecule, e and m denote the charge and the mass of the electron, see [19]. We know that lim n→∞ ‖vn‖2Φ = ‖v‖2Φ. By Brézis-Lieb lemma again, we have lim n→∞ ‖vn‖2Φ − lim n→∞ ‖vn − v‖2Φ = ‖v‖2Φ, which implies lim n→∞ ‖vn − v‖2Φ = 0.	cache/ejde-123.pdf	txt/ejde-123.txt