Global bifurcation curves of nonlocal elliptic equations with oscillatory nonlinear term

2023/09/26 by Shibata, Tetsutaro
#34C23 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2309.14714

Abstract

We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with oscillatory nonlinear term. We establish the precise asymptotic formulas for the bifurcation curves λ(α) as α→ ∞ and α→ 0, where α:= \Vert u_λ\Vert_∞ and u_λ is the solution associated with λ. We show that the second term of λ(α) is oscillatory as α→ ∞.

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