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Diffstat (limited to 'source/know/concept/gronwall-bellman-inequality')
| -rw-r--r-- | source/know/concept/gronwall-bellman-inequality/index.md | 7 |
1 files changed, 4 insertions, 3 deletions
diff --git a/source/know/concept/gronwall-bellman-inequality/index.md b/source/know/concept/gronwall-bellman-inequality/index.md index 5fd9f38..417b033 100644 --- a/source/know/concept/gronwall-bellman-inequality/index.md +++ b/source/know/concept/gronwall-bellman-inequality/index.md @@ -1,5 +1,6 @@ --- title: "Grönwall-Bellman inequality" +sort_title: "Gronwall-Bellman inequality" # sic date: 2021-11-07 categories: - Mathematics @@ -28,7 +29,7 @@ $$\begin{aligned} <div class="accordion"> <input type="checkbox" id="proof-original"/> <label for="proof-original">Proof</label> -<div class="hidden"> +<div class="hidden" markdown="1"> <label for="proof-original">Proof.</label> We define $w(t)$ to equal the upper bounds above on both $w'(t)$ and $w(t)$ itself: @@ -86,7 +87,7 @@ $$\begin{aligned} <div class="accordion"> <input type="checkbox" id="proof-integral"/> <label for="proof-integral">Proof</label> -<div class="hidden"> +<div class="hidden" markdown="1"> <label for="proof-integral">Proof.</label> We start by defining $w(t)$ as follows, which will act as shorthand: @@ -153,7 +154,7 @@ $$\begin{aligned} <div class="accordion"> <input type="checkbox" id="proof-special"/> <label for="proof-special">Proof</label> -<div class="hidden"> +<div class="hidden" markdown="1"> <label for="proof-special">Proof.</label> Starting from the "ordinary" Grönwall-Bellman inequality, the fact that $\alpha(t)$ is non-decreasing tells us that |