The fundamental gap for a one-dimensional Schrödinger operator with Robin boundary conditions

DOI10.1090/proc/15140OpenAlexW3043268934MaRDI QIDQ5858376

Daniel Hauer, Ben Andrews, Julie Clutterbuck

Publication date: 13 April 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.06900

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenvalue problems for linear operators (47A75) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15) Boundary eigenvalue problems for ordinary differential equations (34B09)

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Cites Work

• Spectral analysis of nonlinear operators
• The maximum principle
• Global bifurcation from the eigenvalues of the \(p\)-Laplacian
• Sturm-Liouville theory for the radial \(\Delta_p\)-operator
• On the generalization of the Courant nodal domain theorem
• Spectral gaps and rates to equilibrium for diffusions in convex domains
• Non-concavity of the Robin ground state
• Eigenvalue problems for the \(p\)-Laplacian
• Numerical Methods for Large Eigenvalue Problems
• Proof of the fundamental gap conjecture
• Optimal Lower Bound for the Gap Between the First Two Eigenvalues of One-Dimensional Schrodinger Operators with Symmetric Single-Well Potentials
• The Eigenvalue Gap for One-Dimensional Convex Potentials
• On the first two eigenvalues of Sturm-Liouville operators
• The Robin Laplacian—Spectral conjectures, rectangular theorems

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