id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1411	Wang, Tao; Tian, Xiaoyu; He, Wenling	New type of multi-bump solutions for Schrodinger-Poisson systems	2025	14	.pdf	application/pdf	6587	366	88	U pe−x1 ; • H1(R3) is the usual Sobolev space endowed with inner product (u, v) = ∫ R3(∇u∇v+uv)dx and norm ∥u∥2 = ∫ R3(|∇u|2 + u2)dx; • D1,2(R3) is the completion of C∞ 0 (R3) with respect to the norm ∥u∥2D1,2 = ∫ R3 |∇u|2dx; • Hk and Dk are symmetric Sobolev subspaces defined by Hk By using Hölder inequality and Sobolev inequality, we obtain ∥Φu∥2D1,2 = ∫ R3 Φuu 2dx ≤	cache/ejde-1411.pdf	txt/ejde-1411.txt