query: Using gronwall's lemma to prove inequalities involving max$x(t)$.
positive_passages.docid: 19658
positive_passages.text: $\max_{t\in[0,T]}|x(t)|^2 \le |x(0)|^2e^{\int_0^T|y|^2\,\mathrm ds}.$ using gronwall's lemma?
negative_passages.docid: 58629
negative_passages.text: Show that the $\max{ \{ x,y \} }= \frac{x+y+|x-y|}{2}$.
negative_passages.docid: 62428
negative_passages.text: How to prove this inequality in Banach space?
negative_passages.docid: 35001
negative_passages.text: Prove inequality using Schwarz's Lemma
negative_passages.docid: 7775
negative_passages.text: Show that $|x-y|\leq |x|+|y|$.
negative_passages.docid: 33617
negative_passages.text: Prove the inequality involving multiple integrals
negative_passages.docid: 117262
negative_passages.text: Proving a logarithm inequality
negative_passages.docid: 126032
negative_passages.text: Proving a certain inequality
negative_passages.docid: 70067
negative_passages.text: Asymptotics of $\max\limits_{1\leqslant k\leqslant n}X_k/n$
negative_passages.docid: 13228
negative_passages.text: Proofs of AM-GM inequality
negative_passages.docid: 48593
negative_passages.text: Proof that if $s_n \leq t_n$ for $n \geq N$, then $\liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n$
negative_passages.docid: 33097
negative_passages.text: Proving an inequality without an integral: $\frac {1}{x+1}\leq \ln (1+x)- \ln (x) \leq \frac {1}{x}$
negative_passages.docid: 20863
negative_passages.text: how do I prove this inequallity?
negative_passages.docid: 34398
negative_passages.text: Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
negative_passages.docid: 29679
negative_passages.text: Prove: $|x-y|\leq |x|+|y|$
negative_passages.docid: 123478
negative_passages.text: Generalized Poincaré Inequality on H1 proof.
negative_passages.docid: 67292
negative_passages.text: Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$