Revision #625 → #1473 · back to history
addedPicard–Lindelöf theorem (local existence and uniqueness)c635baef5c9a
addedInitial value problem (IVP)d56b5bff1ba7
addedSolutions of the ODE satisfy the integral equation275d37c1058f
addedPicard operator Γ1c595032dfba
addedPicard iterates converge to a solution of the IVPd6a00acf7d95
addedBanach fixed-point theorem (contraction mapping theorem)bf2fb6e0633c
addedPicard operator is a contraction (after restricting the interval)220b90e3a80a
addedIterate bound for the Picard operator (Γᵐ)7ddd5897d338
addedIterate corollary of Banach fixed-point (Tⁿ contraction ⇒ T has unique fixed point)6e91a719b3b2
addedPicard–Lindelöf for C¹ vector fields (existence of integral curve)450f97ed9c8c
addedPeano existence theorem82a36414e4a6
addedCounter-example: dy/dt = y^{1/3} (continuous but not Lipschitz) has three solutionsab729fb266a5
addedCarathéodory's existence theoremf564df550648
addedOkamura's theorem (necessary & sufficient uniqueness criterion)f5ebe73bcf48
addedGlobal existence for globally Lipschitz vector fields207070795c12
addedCounter-example: locally Lipschitz dy/dt = y² blows up in finite time52980a2f163e
addedIntegral curves on a compact manifold exist for all timea4345b9ef198
addedCounter-example: non-uniqueness when Lipschitz fails (dy/dt = a·y^{2/3})b5367183006f