id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-121	El Mokhtar, Mohammed El Mokhtar Ould	Existence of solutions for singular elliptic problems with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent 	2023	11	.pdf	application/pdf	4093	238	86	= (1/2)‖un‖2µ − (1/2∗) ∫ Ω h(x)|x|−2∗b|un|2∗ dx − λ 1− γ ∫ Ω (u+ n + θ)1−γ − θ1−γ |x|β dx = c+ on(1) and 〈J ′λ(un), un〉 = ‖un‖2µ − ∫ Ω h(x)|x|−2∗b|un|2∗ dx− λ ∫ Ω (u+ n + θ)1−γ − θ1−γ |x|β dx = on(1), for n large, where on(1) denotes on(1)→ 0 as n→∞. Then c+ on(1) = Jλ(un)− 1 2∗ 〈J ′λ(un), un〉 ≥ (1 2 − 1 2∗ ) ‖un‖2µ − λ ( 1 1− γ − 1 2∗ ) ∫ Ω (u+ n + θ)1−γ − θ1−γ |x|β dx ≥ (1 2 − 1 2∗ ) ‖un‖2µ dx ) 2(N−β) 2∗(N−β)+N , with C(π,R) = ( 2π N 2 (N − β(2∗(N−β)+N) 2∗(N−β)−N+2β )Γ(N2 ) ) 2∗(N−β)−N+2β 2∗(N−β)+N ( RN− β(2∗(N−β)+N) 2∗(N−β)−N+2β ) 2∗(N−β)−N+2β 2∗(N−β)+N and N − β[2∗(N − β) +N ] 2∗(N − β)−N + 2β = (N − β)[2∗(N − β)−N ] 2∗(N − β)−N + 2β > 0.	cache/ejde-121.pdf	txt/ejde-121.txt