Limiting classification on linearized eigenvalue problems for 1-dimensional Allen-Cahn equation. I. Asymptotic formulas of eigenvalues

DOI10.1016/j.jde.2015.01.023zbMath1319.34152OpenAlexW2054224830MaRDI QIDQ2339462

Shoji Yotsutani, Tohru Wakasa

Publication date: 1 April 2015

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2015.01.023

zbMATH Keywords

Lamé equationelliptic integralsasymptotic formulas of eigenvalueslinearized eigenvalue problemsrepresentation of eigenfunctions

Mathematics Subject Classification ID

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (5)

Secondary bifurcation for a nonlocal Allen-Cahn equation ⋮ Stability for stationary solutions of a nonlocal Allen-Cahn equation ⋮ Limiting classification on linearized eigenvalue problems for 1-dimensional Allen-Cahn equation. II: Asymptotic profiles of eigenfunctions. ⋮ Asymptotic formulas of the eigenvalues for the linearization of a one-dimensional sinh-Poisson equation ⋮ Exact eigenvalues and eigenfunctions for a one-dimensional Gel’fand problem

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