On 1-Laplacian elliptic problems involving a singular term and an L1-data

In this paper, we look at the problem - Δ p u + | ∇ u | p = f h ( u ) in Ω , u ≥ 0 in Ω , u = 0 on ∂ Ω , with Ω is a bounded open subset of R N with Lipschitz boundary, Δ p u is the p -laplacian operator for 1 ≤ p < N , f ∈ L 1 ( Ω ) is nonnegative and h is a continuous function that may be singu...

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Bibliographic Details
Published in:Journal of elliptic and parabolic equations 2023-06, Vol.9 (1), p.501-533
Main Authors: El Hadfi, Youssef, El Hichami, Mohamed
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Partial Differential Equations
Online Access:Get full text
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Summary:In this paper, we look at the problem - Δ p u + | ∇ u | p = f h ( u ) in Ω , u ≥ 0 in Ω , u = 0 on ∂ Ω , with Ω is a bounded open subset of R N with Lipschitz boundary, Δ p u is the p -laplacian operator for 1 ≤ p < N , f ∈ L 1 ( Ω ) is nonnegative and h is a continuous function that may be singular at s = 0 + . We will demonstrate the existence of solutions in the case 1 ≤ p < N . Moreover, if p = 1 , f > 0 and h is decreasing, we will show the uniqueness of the solutions.
ISSN:2296-9020
2296-9039
DOI:10.1007/s41808-023-00210-2