id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-220	Recova, Leandro L.; Rumbos, Adolfo J.	An asymmetric problem at resonance with a one-sided Ahmad-Lazer-Paul condition	2021	20	.pdf	application/pdf	8417	340	72	Let Ω be a bounded, connected, open subset of RN , for N ≥ 2, with smooth boundary ∂Ω. Consider the Dirichlet problem −∆u = λku+ g(x, u), x ∈ Ω; u = 0, x ∈ ∂Ω, (1.1) where λk is an eigenvalue of the N -dimensional Laplacian −∆ in Ω with Dirichlet boundary conditions, and g : Ω × R → R is continuous and uniformly bounded; that is, |g(x, s)| 6M, for all x ∈ Ω, and s ∈ R, (1.2) 2010 Mathematics Subject Classification. − 2G(x, um)] dx ∣∣∣ 6 C + εm(‖u+ m‖+ ‖u−m‖), for all m. (3.4) Put T (x, s) = g(x, s)s − 2G(x, s), for x ∈ Ω and s ∈ R.	cache/ejde-220.pdf	txt/ejde-220.txt