Existence of strictly positive solutions for sublinear elliptic problems\n in bounded domains

2013/04/17 by T. Godoy, Godoy, Tomas, Uriel Kaufmann +1
Computer Science · Mathematics · #35B09 #35J25 #35J61 #35J65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1304.4883

openalex publication_date 2013/04/17 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28

Abstract

Let \Ω be a smooth bounded domain in \ℝ^N and let m be a\npossibly discontinuous and unbounded function that changes sign in \Ω.\nLet f:\[ 0,\∞\) \→\[ 0,\∞\) be a\ncontinuous function such that k₁\ξ^p\≤ f\(\ξ\) \≤\nk₂\ξ^p for all \ξ\≥0 and some k₁,k₂>0 and\np\∈\(0,1\) . We study existence and nonexistence of strictly\npositive solutions for nonlinear elliptic problems of the form -\Δν=m\(x\) f\(u\) in \Ω, u=0 on \∂\Ω.\n

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