Electron. J. Differential Equations, Vol. 2026 (2026), No. 39, pp. 1-13.

Discretisation of the Ermakov-Painleve II equation: Dirichlet and Robin-type boundary value problems

Pablo Amster, Colin Rogers

Abstract:
Two-point boundary value problems for a discrete Ermakov-Painle-v\'e II equation are analysed by means of topological methods. In addition, an alternative variational approach is detailed. Existence of solutions is established for appropriate choice of parameters.

Submitted December 3, 2025. Published June 8, 2026.
Math Subject Classifications: 39A27, 34B15.
Key Words: Ermakov-Painleve II equation; Difference equations; Dirichlet boundary conditions; nonlinear Robin conditions.
DOI: 10.58997/ejde.2026.39

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Pablo Amster
Departamento de Matemática
Facultad de Ciencias Exactas y Naturales
Universidad de Buenos Aires, and
IMAS - CONICET, Ciudad Universitaria, Pabell&oaccute;n I
(1428) Buenos Aires, Argentina
email: pamster@dm.uba.ar
Colin Rogers
School of Mathematics and Statistics
The University of New South Wales
Sydney, NSW 2052, Australia
email: c.rogers@unsw.edu.au

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