id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-610	Wang, Lixia; Zhao, Pingping; Zhang, Dong	Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations	2024	12	.pdf	application/pdf	4980	230	73	By (1.3) and the Gateaux derivative of I, we can obtain that ‖un − u‖2 = 〈I ′(un)− I ′(u), un − u〉+ V0 ∫ R3 (un − u)2 dx+ 2ω ∫ R3 (φunun − φuu)(un − u) dx + ∫ R3 (h(x, un)− h(x, u))(un − u) dx+ ∫ R3 (φ2 un un − φ2 uu)(un − u) dx By an easy computation, we obtain that 〈 [(φ2 un un − φ2 uu)(un − u) dx ∣∣ ≤ |φ2 un un − φ2 uu|3/2|un − u|3 ≤ (|φ2 un un|3/2 + |φ2 uu|3/2)|un − u|3 → 0, as n→ +∞. By Proposition 2.3 and un → u in Ls(R3) for 2 ≤ s < 6, we have∫ R3 (h(x, un)− h(x, u))(un − u)	cache/ejde-610.pdf	txt/ejde-610.txt