id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-820	Tarek Saanouni, Tarek	Existence of non-global solutions to bi-harmonic inhomogeneous nonlinear Schrodinger equations without gauge invariance	2024	11	.pdf	application/pdf	4341	308	87	|x|−τ/p|u|ψ q p R dx dt ≲ R τ p−4 (∫ R4 R4 2 ∫ B(R) |x|−τ |u|pψq R dx dt )1/p∣∣[R4 2 , R4]×B(R) So, (3.7) and (3.9) imply that −i ∫ T 0 ∫ RN w∂tv dx dt = lim n ∫ T 0 ∫ RN ( −∆2wn + λ|x|−τ |un|p ) v dx dt = − lim n ∫ T 0 ∫ RN wn∆ 2v dx dt + λ lim n ∫ T 0 ∫ RN |x|−τ |un|pv dx dt. (3.11)	cache/ejde-820.pdf	txt/ejde-820.txt