From 77bbbc0d941b926a781f06a3f2147fb5dc8f8514 Mon Sep 17 00:00:00 2001 From: salagne Date: Sun, 5 Jul 2020 00:14:38 +0200 Subject: [PATCH] minor changes --- ana18.tex | 4 ++-- analysisII.pdf | Bin 863389 -> 863395 bytes 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/ana18.tex b/ana18.tex index 560eaa4..e50f98e 100644 --- a/ana18.tex +++ b/ana18.tex @@ -113,7 +113,7 @@ ,\] folgt $y(t) = v(t)$ auf dem gemeinsamen Existenzintervall $I$. \end{proof} -\begin{satz}[Existenzsatz von Picard-Linderlöf] +\begin{satz}[Existenzsatz von Picard-Lindelöf] Sei $f\colon D \to \R^{n}$ stetig, lokal Lipschitz-stetig bezüglich $x$. Dann gilt $\forall (t_0, y_0) \in D$, $\exists \epsilon > 0$ und eine Lösung der AWA \begin{align*} @@ -184,7 +184,7 @@ y^{k}(t) \coloneqq y_0 + \int_{t_0}^{t} f(s, y^{k-1}(s)) \d s \xrightarrow{k \to \infty} \text{Lösung der AWA} .\end{align*} - \item Ohne die Forderung der Lipschitz-stetigkeit geht die Eindeutigkeit der Lösung verloren + \item Ohne die Forderung der Lipschitz-Stetigkeit geht die Eindeutigkeit der Lösung verloren (siehe Beispiel \ref{bsp:dgl-uneindeutig}), aber die Existenz gilt nach dem Satz von Peano immer noch. \end{enumerate} diff --git a/analysisII.pdf b/analysisII.pdf index 86a3b1924e24ae25eee84e8c155989a05e878a71..e46854acf28878722a42934e94b3b791cfece9f9 100644 GIT binary patch delta 10620 zcmaiaWl)?!6DF{@!{Y89SUfn3yCt{;f=dYQ@FI)5LvVLVAR#R71Pe}Zx8MYV!{z(# zuI}#F{phKl=^m+?>F1fAn!H7Ul0|`F7$OV_27)2OP++LdXd0}DLYYu(RCZw3Sk;|U zn6UFme{4@qPtE5XHRV!|{qqi6hN+oxvg5*K2p@ZNhLQ-=u3g}-_0ISn7u2jn-^rAA z=YEdzl#(V``6n%9@GBhN z7-q%Poz?D`&4-eAv}c?&acMw?mONBVXy@*}) z32xL1YJL2tf{Pu7z8|Wh=B=Z?LeemcvoB{9qB^lGQkcW z_L#*lkLk$XW7ILIpIf;FX|43WQ~3juxC--tC=eDkhKIZPu+W>4iKC;H5-o0MMKHuw z#bEEM!$=tv*bOo+ErDrxeWS=J-6(H-P9>YFLQn6*r-}rxpJW(%8ZhEy72<832-coL z5|E{LzIwO)qRY2Yc(#3U`0ChIe-3^*L3jzz$%UdcPW4;Y_RU%@W+M{R?#a36=Bz*F zuct|nZTjA)St3Cvy=J>+M zS5|Q!C&X_x%iUl00z?ZYNNO$u;OBUMolTXppmGMS!bgW&SnUO`BGmdKclV3lhF#1N z!>tU!q`N=n(~~WZ84TkV#g^^@ha^16Z?A46;(*b z2=`tc=d@}vAe`bTpTG80h2(NNLOBCfc%d3^%q7TTm{4W| z$jJ@LF|laMu=bEC($c9zqvDxYl0U=6!!9Wnp}V@|7h=)FZ)Vk)I5S=<>5bXA))?N% zJZb-M<74%6_{3<<+$iv+&FP*WHYON)$!e^AAsyi(woP{m4q?|_%U~~G2eX!KFh55 zYs_s-6r=6Lp8O1~LH_h@{9abB@RONEwSXIAjwM=))waBp`b*Y?UL7p%C{A@J_Vxp> zWXJ1G8LkQ2eVQc+-dz9gpH(&&uUXL=OqPVGdFpBJepYPHIl)aH@UER)0I!F`L4v%2 zUB7VENBed%z(t4W{Rw?2+b>;2U{no*Do(!*vf;MUmaH~|8uNoI3Y{y4BP)$Vz={I> z^^@#gj2gO4UP>u>FUszZ{b4J7svcT8MSKnj3WDG#H~naid?{#bVG>0%!G0xtHa2GW zwMXn$Qu(*05yJ`vZRBXJO+f~F3WU$Zq=d-uzYwM^2ve~oY&R|xO53pw0CGY zXtyWr*_O-Omo@yBYd(thCnTO+8y0Hveerh?()~Q*oCYm#((;W(M|i9JK=hrq^!b-z zal#Eks{KfyD9_Gk4PUYjv{EF01pWk$xC9f%>5W$)1Bo%OaIvH!lvj6L{#~sg^MQdX1|W z`mQlNFNUE4ohzEsJ&|oF3G^ZDn(-4U8ge+Ycd3s5rbL1bw zD}-jmxhz--Dm+NyMWAzxc7t9+)}^jnnrT(0pB=ZhHZ!yxqqTeZYuMu&64r-5aC@5Q z48sZc?61X-H$Jue0s!YiOTTDVU2_S^CSGX9uZ4E>eaPXyy@4hC(-hoYEVG znR4-*d%jtP<9u33m0Y*v<^wL$OCUlA_<-a|tb=ZSiEja(H=RRuu8`612aC^aK|7v@$; 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