Theorems · Theorem · ordinary differential equations

ODE_solution_unique_of_eventually

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {v : ℝ → E → E} {s : ℝ → Set E} {K : NNReal}
  {f g : ℝ → E} {t₀ : ℝ},
  (∀ᶠ (t : ℝ) in nhds t₀, LipschitzOnWith K (v t) (s t)) →
    (∀ᶠ (t : ℝ) in nhds t₀, HasDerivAt f (v t (f t)) t ∧ f t ∈ s t) →
      (∀ᶠ (t : ℝ) in nhds t₀, HasDerivAt g (v t (g t)) t ∧ g t ∈ s t) → f t₀ = g t₀ → f =ᶠ[nhds t₀] g

Local uniqueness of ODE solutions.

Defined in

Mathlib.Analysis.ODE.ExistUnique

Cited by

1 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace