A discretisation of the Ermakov-Painlev\'e II equation: Dirichlet and Robin-type boundary value problems
Pablo Amster, Colin Rogers
TL;DR
This paper investigates boundary value problems for a discrete Ermakov-Painlevé II equation using topological and variational methods, establishing the existence of solutions under certain parameters.
Contribution
It introduces a discretisation of the Ermakov-Painlevé II equation and applies novel topological and variational techniques to analyze boundary value problems.
Findings
Existence of solutions for Dirichlet and Robin boundary conditions.
Application of topological methods to discrete nonlinear equations.
Development of an alternative variational approach.
Abstract
Two-point boundary value problems for a discrete Ermakov-Painlev\'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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Fractional Differential Equations Solutions · Nonlinear Differential Equations Analysis