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Morse Index Theorem for Sturm-Liouville Operators on the Real Line by Yang, Ran; Xing, Qin is a scholarly article available to read on EtoBox.

What is Morse Index Theorem for Sturm-Liouville Operators on the Real Line about?

The classical Morse index theorem establishes a fundamental connection between the Morse index-the number of negative eigenvalues that characterize key spectral properties of linear self-adjoint differential operators-and the count of corresponding conjugate points. In this paper, we extend these foundational results to the Sturm-Liouville operator on $\mathbb{R}$. In particular, for autonomous Lagrangian systems, we employ a geometric argument to derive a lower bound for the Morse index. As concrete applications, we establish a criterion for detecting instability in traveling waves within gradient reaction-diffusion systems.

Author

Yang, Ran; Xing, Qin

Published

2025

Language

EN