Asymptotic behavior of bifurcation curves of one-dimensional nonlocal elliptic equations

2021/12/21 by Tetsutaro Shibata, Shibata, Tetsutaro
Mathematics · #34C23 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2112.10995

openalex publication_date 2021/12/21 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We study the one-dimensional nonlocal elliptic equation -(∫₀¹ \vert u(x)\vert^p dx + b)^q u''(x) amp;=amp; λu(x)^p, x ∈ I:= (0,1), u(x) gt; 0, x∈ I,
u(0) amp;=amp; u(1) = 0, where b ≥ 0, p ≥ 1, q > 1 - (1)/(p) are given constants and λ> 0 is a bifurcation parameter. We establish the global behavior of bifurcation diagrams and precise asymptotic formulas for u_λ(x) as λ→ ∞.

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