Sturm–Picone comparison theorem

<h2 id="notes">Notes</h2>

<ul><li>Diaz, J. B.; <a href="/facts/Joyce_McLaughlin/SUvbBmlI">McLaughlin, Joyce R.</a> <i>Sturm comparison theorems for ordinary and partial differential equations</i>. Bull. Amer. Math. Soc. 75 1969 335–339 <a href="https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-75/issue-2/Sturm-comparison-theorems-for-ordinary-and-partial-differential-equations/bams/1183530292.full">[1]</a></li>
<li><a href="/facts/Heinrich_Guggenheimer/m19EfKrF">Heinrich Guggenheimer</a> (1977) <i>Applicable Geometry</i>, page 79, Krieger, Huntington <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-88275-368-1 .</li>
<li><a href="/facts/Gerald_Teschl/tEBmvGQA">Teschl, G.</a> (2012). <a href="https://www.mat.univie.ac.at/~gerald/ftp/book-ode/"><i>Ordinary Differential Equations and Dynamical Systems</i></a>. <a href="/facts/Providence%2c_Rhode_Island/77kh9zJT">Providence</a>: <a href="/facts/American_Mathematical_Society/fr5gotCt">American Mathematical Society</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-8218-8328-0.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>C. Sturm, Mémoire sur les équations différentielles linéaires du second ordre, J. Math. Pures Appl. 1 (1836), 106–186 <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>M. Picone, Sui valori eccezionali di un parametro da cui dipende un'equazione differenziale lineare ordinaria del second'ordine, Ann. Scuola Norm. Pisa 11 (1909), 1–141. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Hinton, D. (2005). "Sturm's 1836 Oscillation Results Evolution of the Theory". Sturm-Liouville Theory. pp. 1–27. doi:10.1007/3-7643-7359-8_1. ISBN 3-7643-7066-1. <a href="3-7643-7066-1" target="_blank">3-7643-7066-1</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>For an extension of this important theorem to a comparison theorem involving three or more real second order equations see the Hartman–Mingarelli comparison theorem where a simple proof was given using the Mingarelli identity <a href="/w/index.php?title=Hartman%E2%80%93Mingarelli_comparison_theorem&action=edit&redlink=1" target="_blank">/w/index.php?title=Hartman%E2%80%93Mingarelli_comparison_theorem&action=edit&redlink=1</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
</ol>

Sturm–Picone comparison theorem open-in-new

Sturm–Picone comparison theorem