Quasilinear elliptic problems with singular and homogeneous lower order terms. (February 2019)

• Record Type: Journal Article
• Authors: Carmona, José; Leonori, Tommaso; López-Martínez, Salvador; Martínez-Aparicio, Pedro J.
• Is Part Of: Nonlinear analysis. Volume 179(2019)
• Page Start: 105
• Page End: 130
• Publication Date: 2019-02
• Subjects: 35P30 -- 35J25 -- 35J62 -- 35J75 -- 35B32; Quasilinear elliptic equations -- Singular problems -- Eigenvalue problems; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.08.002
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We deal with singular quasilinear elliptic equations, namely − Δ u = λ u + μ ( x ) | ∇ u | q u q − 1 + f ( x ) in Ω, u > 0 in Ω, u = 0 on ∂ Ω, where Ω is a bounded smooth domain of R N ( N ≥ 3 ), λ ∈ R, 1 < q ≤ 2, 0 ≤ μ ∈ L ∞ ( Ω ) and 0 ≤ f ∈ L p ( Ω ) for some p > N 2 . 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 .