Necessary conditions for Liouvillian solutions of (third order) linear differential equations

DOI10.1007/BF01270928zbMath0813.12003MaRDI QIDQ1340506

Felix Ulmer, Michael F. Singer

Publication date: 6 June 1995

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

zbMATH Keywords

existencesingular pointsdifferential Galois groupLiouvillian solutionsthird order linear differential equation

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Linear ordinary differential equations and systems (34A30) Differential algebra (12H05)

Related Items (17)

An algorithm for computing invariants of differential Galois groups ⋮ Linear differential equations and products of linear forms ⋮ Constructing a third-order linear differential equation ⋮ On the Liouvillian solutions to the perturbation equations of the Schwarzschild black hole ⋮ Liouvillian solutions of third order differential equations ⋮ Liouvillian solutions of linear differential equations of order three and higher ⋮ Extensions of differential representations of SL₂ and tori ⋮ Non-integrability of the Kepler and the two-body problems on the Heisenberg group ⋮ Differential Galois approach to the non-integrability of the heavy top problem ⋮ Zariski closures of reductive linear differential algebraic groups ⋮ Non-existence of Liouvillian solutions for a free quantum particle on a torus surface. I: Polar states ⋮ Nonintegrability of Bianchi VIII Hamiltonian system ⋮ Swinging Atwood Machine: experimental and numerical results, and a theoretical study ⋮ Differential equations and finite groups ⋮ Classes of elementary function solutions to the CEV model I ⋮ Nonintegrability of the Suslov problem ⋮ Note on algebraic solutions of differential equations with known finite Galois group

Uses Software

• Cayley

Cites Work

• Moduli of linear differential equations on the Riemann sphere with fixed Galois groups
• An algorithm for solving second order linear homogeneous differential equations
• On Liouvillian solutions of linear differential equations
• On solutions of linear ordinary differential equations in their coefficient field
• Kovacic's algorithm and its application to some families of special functions
• Galois groups of second and third order linear differential equations
• Liouvillian and algebraic solutions of second and third order linear differential equations
• Effective procedures in field theory
• Solving Homogeneous Linear Differential Equations in Terms of Second Order Linear Differential Equations
• Solution of the Inverse Problem of Differential Galois Theory in the Classical Case
• Algebraic Groups and Algebraic Dependence
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