Non-singular solutions of p-Laplace problems, allowing multiple changes of sign in the nonlinearity

2020/09/02 by Philip Korman, Korman, Philip
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2009.01304

openalex publication_date 2020/09/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

For the p-Laplace Dirichlet problem (where φ(t)=t|t|^p-2, p>1) \[ φ(u'(x))'+ f(u(x))=0 \mboxfor -1(p-1)(f(u))/(u)>0 for u>γ>0, while ∫_u^γf(t) dt < 0 for all u ∈ (0,γ). Then any positive solution, with max_(-1,1) u(x)=u(0)>γ, is non-singular, no matter how many times f(u) changes sign on (0,γ). Uniqueness of solution follows.

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