Sufficient and Necessary Conditions on the Existence and Estimates of Boundary Blow-Up Solutions for Singular p-Laplacian Equations

Let Ω denote a smooth, bounded domain in ℝ N ( N ≥ 2). Suppose that g is a nondecreasing C 1 positive function and assume that b ( x ) is continuous and nonnegative in Ω, and that it may be singular on ∂Ω. In this paper, we provide sufficient and necessary conditions on the existence of boundary blo...

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Bibliographic Details
Published in:Acta mathematica scientia 2023-05, Vol.43 (3), p.1175-1194
Main Authors: Zhang, Xuemei, Kan, Shikun
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:Let Ω denote a smooth, bounded domain in ℝ N ( N ≥ 2). Suppose that g is a nondecreasing C 1 positive function and assume that b ( x ) is continuous and nonnegative in Ω, and that it may be singular on ∂Ω. In this paper, we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p -Laplacian problem The estimates of such solutions are also investigated. Moreover, when b has strong singularity, the nonexistence of boundary blow-up (radial) solutions and infinitely many radial solutions are also considered.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-023-0311-4