A Non-Existence Result for Positive Periodic Solutions to the Relativistic Singular Liénard Equation

Ruina Zhao

doi:https://doi.org/10.14445/22315373/IJMTT-V71I6P107

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 6 | Year 2025 | Article Id. IJMTT-V71I6P107 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I6P107

A Non-Existence Result for Positive Periodic Solutions to the Relativistic Singular Liénard Equation

Ruina Zhao

Received	Revised	Accepted	Published
17 Apr 2025	30 May 2025	17 Jun 2025	30 Jun 2025

Citation :

Ruina Zhao, "A Non-Existence Result for Positive Periodic Solutions to the Relativistic Singular Liénard Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 6, pp. 74-80, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I6P107

Abstract

In this paper, we establish the non-existence of positive periodic solutions to the attractive singular Liénard equation with relativistic acceleration ( 𝑥′√1−𝑥′2𝑣2) ′+𝑓(𝑥)𝑥′+𝑎(𝑡)𝑥𝜇+𝑏(𝑡)𝑥𝜌=𝑠 Where 𝑣 is the speed of light in a vacuum? Distinct from the classical Liénard equation, the inertial term arises from the relativistic momentum, which introduces strong nonlinearity and imposes a natural velocity bound.

Keywords

Attractive singularity, Liénard equation, Non-existence, Relativistic acceleration.

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