Large solutions of semilinear equations with Hardy potential

2020/06/04 by Moshe Marcus, Marcus, Moshe
Computer Science · Mathematics · #35J10 #35J60 (Primary) 35J75 #35J66 (Secondary) #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.02993

openalex publication_date 2020/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider equations of the form -L_μu +f(u)=0 in a smooth domain Ω, where L_μ=Δ+ μδ^-2 and δ(x) denotes the distance of the point x to the boundary of the domain. The nonlinear term f is positive, increasing and convex on (0,∞), satisfies the Keller-Osserman condition and some additional technical assumptions. The conditions are satisfied, in particular, by power and exponential nonlinearities. We discuss the question of existence and uniqueness of large solutions when μ>0.

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