id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-290	Alvarez-Caudevilla, Pablo; Colorado, Eduardo; Ortega, Alejandro	Existence of positive solutions for Brezis-Nirenberg type problems involving an inverse operator	2021	24	.pdf	application/pdf	10098	499	76	Introduction In this work, we analyze the existence of positive solutions of the second order elliptic equation under homogeneous Dirichlet boundary conditions and involving a non-local term, −∆u = γ(−∆)−1u+ |u|p−1u in Ω, u = 0 on ∂Ω, (1.1) where γ is a positive real parameter and Ω is a smooth bounded domain of RN , with N ≥ 3, 1 < p ≤ 2∗ − 1, where 2∗ = 2N N−2 is the critical Sobolev exponent. Here, as customary (−∆)−1u = v, if −∆v = u in Ω, v = 0 on ∂Ω. Thus, (−∆)−1 is a positive linear integral compact operator from L2(Ω) into itself, which is well-defined thanks to the Spectral Theorem.	cache/ejde-290.pdf	txt/ejde-290.txt