2 papers
math.CA2025
The Degenerate Third Painleve' Equation: Complete Asymptotic Classification of Solutions in the Neighbourhood of the Regular Singular Point
A. V. Kitaev, A. Vartanian
We give a classification for the small- asymptotic behaviours of solutions to the degenerate third Painlevé equation, $u^{''}(τ) = \frac{(u^{\prime}(τ))^{2}}{u(τ)} - \frac{u^{\p…
math.CA2023
One-Parameter Meromorphic Solution of the Degenerate Third Painlevé Equation with Formal Monodromy Parameter Vanishing at the Origin
A. V. Kitaev, A. Vartanian
We prove that there exists a one-parameter meromorphic solution vanishing at of the degenerate third Painlevé equation, \begin{equation*} u^{\prime \prime}(τ) \! = \!…