On Dirichlet problems with singular nonlinearity of indefinite sign

2014/11/21 by Godoy, Tomás, Kaufmann, Uriel
#34B16 #35B09 #35J25 #35J75 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1411.5875

Abstract

Let Ω be a smooth bounded domain in ℝ^N, N≥1, let K, M be two nonnegative functions and let α,γ>0. We study existence and nonexistence of positive solutions for singular problems of the form -Δu=K( x) u^-α-λM( x) u^-γ in Ω, u=0 on ∂Ω, where λ>0 is a real parameter. We mention that as a particular case our results apply to problems of the form -Δu=m( x) u^-γ in Ω, u=0 on ∂Ω, where m is allowed to change sign in Ω.

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