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

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.