A bifurcation problem for a one-dimensional p-Laplace elliptic problem with non-odd absorption

2022/04/12 by Alexandre N. Carvalho, de Carvalho, Alexandre Nolasco, Tito Luciano Mamani Luna +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.06116

openalex publication_date 2022/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence of solutions of a one-dimensional eigenvalue problem -(|ϕ_x|^p-2ϕ_x)_x=λ(|ϕ|^q-2ϕ-f(ϕ)) such that ϕ(0)=ϕ(1)=0, where p,q>1, λ is a positive real parameter and f is a continuous (not necessarily odd) function. Our goal is to give a complete description of solutions of this problem. We completely characterize the set of solutions of this problem, which may be uncountable. For 1

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