Large solutions of degenerate and/or singular quasilinear elliptic equations in a ball

2022/06/14 by Raj Narayan Dhara, Dhara, Raj Narayan
Computer Science · Mathematics · #35B44 #35B51 #35C99 #35J25 #35J70 #35J92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2206.06707

openalex publication_date 2022/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider local weak large solutions with its blow-up rate near the boundary to certain class of degenerate and/or singular quasilinear elliptic equation \rm div(d^α(x,∂B)Φ_p(∇ u)) = b(x)f(u) in a ball B, where f is normalized regularly varying at infinity with index σ+1>p-1, p>1. In particular, how the asymptotic behavior of the solution changes over the varying index and degeneracy and/ or singularity present in the equation. We also include the second order blow-up rate for the corresponding semilinear problem.

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