id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-398	Dou, Xuechao; Sun, Juntao	Local well-posedness and standing waves with prescribed mass for Schrodinger-Poisson systems with a logarithmic potential in R^2	2023	13	.pdf	application/pdf	4753	317	84	Inspired by [24], Cingolani and Weth [11] developed a variational framework of ((1.3) with W (x) ≡ 0 in the smaller Hilbert space X := { u ∈ H1(R2) : ∫ R2 ln(1 + |x|)u2dx <∞ } , endowed with the norm ‖u‖2X := ∫ R2 (|∇u|2 + u2(1 + ln(1 + |x|2))) dx dy − ∫ R2 F (u) dx. (1.5) under the constraint S(c) := { u ∈ H : ∫ R2 u2dx = c } , where H := { u ∈ H1(R2) : ∫ R2 ln(1 + |x|2)u2dx <∞ } , endowed with the norm ‖u‖H := ‖u‖H1 + ‖u‖∗, here ‖u‖2∗ = ∫ R2 ln(1 + |x|2)u2dx.	cache/ejde-398.pdf	txt/ejde-398.txt