PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
April 26, 2026Proceedings of the Royal Society of Edinburgh Section A Mathematics0 citations

The optimal weight of vibrating string equations with the first two eigenvalues based on critical equations

View Full Paper
JQJiangang QiCSChunyan SunJXJing Xu

Key Points

  • This research aims to determine the optimal weight of vibrating string equations based on given eigenvalues, focusing on conditions for uniqueness.
  • Applied critical equations method in L^p[0,1] for p > 1.
  • Utilized inverse spectral theory related to Sturm–Liouville problems with measure coefficients.
  • Estimated extremum for partial trace of the first two eigenvalues on a sphere in L^1[0,1].
  • Unique determination of optimal weight occurs if and only if λ2 ≥ 2λ1, under non-negative and symmetrical conditions.
  • Provided estimation for the extremum related to the first two eigenvalues on a sphere.

Abstract

The present paper is concerned with the optimal weight of vibrating string equations with the first two eigenvalues ₁ and ₂ being given. Applying the method of critical equations in Lᵖ0, 1 for p 1 and the inverse spectral theory of Sturm–Liouville problems with measure coefficients, we find that the optimal weight can be uniquely determined if and only if ₂ 2₁ provided that the weight is non-negative and symmetrical. As an application, we provide an estimation of the extremum for partial trace of the first two eigenvalues on a sphere in L¹0, 1.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Qi et al. (2026) studied this question.

synapsesocial.com/papers/69edabb84a46254e215b38f4https://doi.org/10.1017/prm.2026.10151
Ask AI
Helpful
Bookmark
Share
View Full Paper