Precise Asymptotics for Bifurcation Curve of Nonlinear Ordinary Differential Equation
Tetsutaro Shibata · Mathematics · 2020
We study the following nonlinear eigenvalue problem −u″(t)=λf(u(t)),u(t)>0,t∈I:=(−1,1),u(±1)=0, where f(u)=log(1+u) and λ>0 is a parameter. Then λ is a continuous function of α>0, where α is the maximum norm α=∥uλ∥∞ of the solution uλ associated with λ. We establish the precise asymptotic formula for λ=λ(α) as α→∞ up to the third term of λ(α).