Differential Equations

This group gathers theorems from the analytic theory of differential equations, the results that guarantee when a differential equation has a solution, when that solution is unique, and how it behaves. It covers the classical existence and uniqueness theorems of Picard-Lindelof, Peano, and Cauchy-Kovalevskaya, Gronwall's inequality used to bound how far solutions can drift apart, the qualitative theory of planar systems, including the Poincare-Bendixson theorem, and further identities and estimates used to establish or rule out the existence of solutions to ordinary and partial differential equations.