On parameterized differential Galois extensions

Abstract

We prove some existence results on parameterized strongly normal extensions for logarithmic equations. We generalize a result in [Wibmer, Existence of d-parameterized Picard-Vessiot extensions over fields with algebraically closed constants, J. Algebra, 361, 2012]. We also consider an extension of the results in [Kamensky and Pillay, Interpretations and differential Galois extensions, Preprint 2014] from the ODE case to the parameterized PDE case.

References in corpus (3)

• Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups
• Contributions to the model theory of partial differential fields
• Some applications of the parameterized Picard-Vessiot theory

Cited by in corpus (3)

• Calculating differential Galois groups of parametrized differential equations, with applications to hypertranscendence
• Calculating Galois groups of third order linear differential equations with parameters
• Differential Galois Theory and Isomonodromic Deformations