id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-315	Wan, Youyan; Tan, Jinggang	Standing waves to Chern-Simons-Schrodinger systems with critical exponential growth	2021	14	.pdf	application/pdf	5311	326	86	4 Y. WAN, J. TAN EJDE-2021/77 Again we can derive from ∂1A2 − ∂2A1 = − 1 2u 2 that∫ R2 A0|u|2 In fact, since ‖un‖ ≤ c0, J(un)→ c, and J ′(un)→ 0, we have∫ R2 F (un) = 1 2 ‖un‖2 + 1 2 ∫ R2 ( A2 1,n|un|2 +A2 2,n|un|2 ) dx− c+ on(1),∫ R2 f(un)un dx = ‖un‖2 + 3 ∫ R2 ( A2 1,n +A2 2,n ) u2 n dx− εn‖un‖, where εn → 0 as n→∞. By Proposition 2.1 and Sobolev embedding theorem, we obtain ∫ R2 F (un) ≤ 1 2 ‖un‖2 + C‖un‖4 − c+ on(1),∫ R2 f(un)un dx = ‖un‖2 + C‖un‖4 − εn‖un‖. From ‖un‖ ≤ c0, we obtain ∫ R2 f(un)un dx ≤ c0 and ∫ R2 F (un) dx ≤ c0.	cache/ejde-315.pdf	txt/ejde-315.txt