<div dir="ltr"><p class="gmail-MsoTitle" style="text-align:center"><span style="font-size:18pt;font-family:"times new roman",serif">SEMINARIO
DI MATEMATICA</span><span style="font-family:"times new roman",serif;font-size:16pt"> </span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif">Giovedì 17 novembre 2016</span><span style="font-size:16pt;font-family:"times new roman",serif"><span></span></span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif">ore 17:00<span></span></span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif"><span> </span></span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><u><span style="font-size:16pt;font-family:"times new roman",serif">Scuola Normale Superiore<span></span></span></u></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif">Pisa<span></span></span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:"times new roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial">Aula Tonelli<span></span></span></p>

<p class="MsoNormal"><b><u><span style="font-size:16pt;font-family:"times new roman",serif"><span><span style="text-decoration:none"> </span></span></span></u></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span style="font-size:24pt;font-family:"times new roman",serif">Luca Battaglia</span></b><b><span style="font-size:24pt;font-family:"times new roman",serif"><span></span></span></b></p>

<p class="MsoNormal" align="center" style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span style="font-size:9.5pt;font-family:arial,sans-serif">(</span><i><span style="font-family:"times new roman",serif">Università Roma La Sapienza)</span></i><span style="font-size:9.5pt;font-family:arial,sans-serif"><span></span></span></p>

<pre style="text-align:center"><b><i><span style="font-size:12pt;font-family:"times new roman",serif;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span> </span></span></i></b></pre>

<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:16pt;font-family:"times new roman",serif">terrà un
seminario dal titolo:<span></span></span></p>

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<pre style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span lang="EN-US" style="font-size:24pt;font-family:"times new roman",serif;color:black">“</span></b><b><span lang="EN-US" style="font-size:24pt;font-family:"times new roman",serif">Groundstate solutions for a nonlinear </span></b></pre><pre style="text-align:center;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span lang="EN-US" style="font-size:24pt;font-family:"times new roman",serif">Choquard equation</span></b><b><span lang="EN-US" style="font-size:24pt;font-family:"times new roman",serif;color:black">”<span></span></span></b></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span lang="EN-US" style="font-size:24pt;font-family:"times new roman",serif;color:black"><span> </span></span></b></pre><pre style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif;color:black">Abstract:<span></span></span></b></pre><pre style="text-align:justify;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">I will discuss the existence of groundstate solutions for the Choquard equation in </span></i></pre><pre style="text-align:justify;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">he whole space R^N. I will first consider the case of a homogeneous nonlinearity F(u)=|u|^p, </span></i></pre><pre style="text-align:justify;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">then I will prove the existence of solutions under general hypotheses. In particular, the cases N = 2 and N >= 3 will have to be treated differently. </span></i></pre><pre style="text-align:justify;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif">The solutions are found through a variational mountain pass strategy.<span></span></span></i></pre><pre style="text-align:justify;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><i><span lang="EN-US" style="font-size:12pt;font-family:"times new roman",serif"><span> </span></span></i></b></pre>

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<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif">Tutti gli interessati sono invitati a
partecipare.<span></span></span></p>

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<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif">Classe di Scienze Matematiche e Naturali<span></span></span></p>

<p class="MsoNormal" style="text-align:justify"><span style="font-size:16pt;font-family:"times new roman",serif"><span> </span></span></p><div><div class="gmail_signature"><div dir="ltr"><div>Valeria Giuliani</div><div>Scuola Normale Superiore</div><div>Servizio alla Didattica e Allievi</div><div>tel. 050 509260</div><div>Piazza dei Cavalieri, 7</div><div>56126 Pisa</div><div>E-mail: <a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a></div><div>E-mail: <a href="mailto:classi@sns.it" target="_blank">classi@sns.it</a></div></div></div></div>
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