Comparison Principle for Elliptic Equations with Mixed Singular Nonlinearities

We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by − Δ p u = f u γ + g u q in Ω , u = 0 on ∂ Ω , where Ω is an open bounded subset of ℝ N where Ω is an open bounded subset of ℝ N , Δ p u := ÷(|∇ u | p − 2 ∇ u ) is the usual p -Laplacian opera...

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Bibliographic Details
Published in:Potential analysis 2022-06, Vol.57 (1), p.83-100
Main Authors: Durastanti, Riccardo, Oliva, Francescantonio
Format: Article
Language:English
Subjects:
Boundary value problems
Elliptic functions
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Potential Theory
Probability Theory and Stochastic Processes
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Summary:We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by − Δ p u = f u γ + g u q in Ω , u = 0 on ∂ Ω , where Ω is an open bounded subset of ℝ N where Ω is an open bounded subset of ℝ N , Δ p u := ÷(|∇ u | p − 2 ∇ u ) is the usual p -Laplacian operator, γ ≥ 0 and 0 ≤ q ≤ p − 1; f and g are nonnegative functions belonging to suitable Lebesgue spaces.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-021-09906-3