Asymptotic behavior of bifurcation curve of nonlinear eigenvalue problem with logarithmic nonlinearity - Shibata, Tetsutaro (Topological Methods in Nonlinear Analysis, 2022)
We study the following nonlinear eigenvalue problem -u’’(t) = λ u(t)^p(1+u(t)), u(t) > 0, t I := (-1,1), u(± 1) = 0, % where p 0 is a given constant and λ > 0 is a parameter. It is known that, for any given α > 0, there exists a unique classical solution pair (λ(α), u_α) with α = u_α_∞. We establish the asymptotic formulas for the bifurcation curves λ(α) and the shape of solution u_α as α → ∞ and α → 0.