We deal with singular quasilinear elliptic equations, namely −Δu=λu+μ(x)[Formula presented]+f(x)inΩ,u>0inΩ,u=0on∂Ω,where Ω is a bounded smooth domain of RN (N≥3), λ∈R, 1<q≤2, 0≤μ∈L∞(Ω) and 0≤f∈Lp(Ω) for some p>[Formula presented]. We completely describe the set of values of the parameter λ for which the problem admits solution. Thus, we study existence, nonexistence and uniqueness of bounded weak solutions in both cases f⪈0 and f≡0.
Quasilinear elliptic problems with singular and homogeneous lower order terms / Carmona, José; Leonori, Tommaso; López-Martínez, Salvador; Martínez-Aparicio, Pedro J.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 179:(2019), pp. 105-130. [10.1016/j.na.2018.08.002]
Quasilinear elliptic problems with singular and homogeneous lower order terms
Carmona, José;Leonori, Tommaso
;
2019
Abstract
We deal with singular quasilinear elliptic equations, namely −Δu=λu+μ(x)[Formula presented]+f(x)inΩ,u>0inΩ,u=0on∂Ω,where Ω is a bounded smooth domain of RN (N≥3), λ∈R, 1| File | Dimensione | Formato | |
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