An initial value problem associated with a Painlevé equation on the positive real axis

DOI10.1016/S0362-546X(97)00049-7zbMath0959.34003OpenAlexW2068669873MaRDI QIDQ4374156

Shun Shimomura

Publication date: 5 March 1998

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(97)00049-7

zbMATH Keywords

Painlevé equationexponentially decreasing Whittaker functionstrigonometric oscillations

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear ordinary differential equations and systems (34A34) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Other functions coming from differential, difference and integral equations (33E30) Asymptotic properties of solutions to ordinary differential equations (34D05) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Cites Work

• The construction of a general solution of a Hamiltonian system with regular type singularity and its application to Painlevé equations
• A family of solutions of a nonlinear ordinary differential equation and its application to Painlevé equations (III), (V) and (VI)
• Contribution à l'étude des solutions de l'équation (V) de Painleve
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