The Dirichlet problem for sublinear elliptic equations with source

2020/09/15 by Kentaro Hirata, Hirata, Kentaro, Adisak Seesanea +1
Computer Science · Mathematics · #31B10 #35B09 (Secondary) #35J91 (Primary) 35J25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2009.06939

openalex publication_date 2020/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a necessary and sufficient condition on nonnegative Radon measures μ and ν for the existence of a positive continuous solution of the Dirichlet problem for the sublinear elliptic equation -Δu=μu^q+ν with prescribed nonnegative continuous boundary data in a general domain. Moreover, two-sided pointwise estimates of Brezis-Kamin type for positive bounded solutions and the uniqueness of a positive continuous L^q-solution are investigated.

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