Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian type equations

2020/09/02 by Alberto Boscaggin, Boscaggin, Alberto, Guglielmo Feltrin +3
Computer Science · Mathematics · #34B15 #34B16 #34B18 #34C25 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2009.00854

openalex publication_date 2020/09/02 · openalex created_date 2020/09/08 · openalex updated_date 2026/07/28

Abstract

The paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the ϕ-Laplacian equation ( ϕ(u') )' + a(t) g(u) = 0, where ϕ is a homeomorphism with ϕ(0)=0, a(t) is a stepwise indefinite weight and g(u) is a continuous function. When dealing with the p-Laplacian differential operator ϕ(s)=|s|^p-2s with p>1, and the nonlinear term g(u)=u^γ with γ∈ℝ, we prove the existence of a unique positive solution when γ∈\mathopen]-∞,(1-2p)/(p-1)\mathclose] ∪ \mathopen]p-1,+∞\mathclose[.

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