<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2019000100001</article-id>
<article-id pub-id-type="doi">10.18273/revint.v37n1-2019001</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[An elliptic equation with random potential and supercritical nonlinearity]]></article-title>
<article-title xml:lang="es"><![CDATA[Una ecuación elíptica con potencial aleatorio y no linealidad supercrítica]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cioletti]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ferreira]]></surname>
<given-names><![CDATA[L. C. F.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Furtado]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade de Brasília Departamento de Matemática ]]></institution>
<addr-line><![CDATA[Brasília ]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidade Estadual de Campinas  ]]></institution>
<addr-line><![CDATA[Campinas ]]></addr-line>
<country>Brazil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<volume>37</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>16</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2019000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2019000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2019000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We are concerned with a nonhomogeneous elliptic equation with random potential and supercritical nonlinearity. Existence of solution is obtained almost surely for a class of potentials that includes continuum and discrete ones. Also, we provide a law of larger numbers for the obtained solutions by independent ensembles and estimate the expected value for their L&#8734;-norms. MSC2010: 47B80, 60H25, 35J60, 35R60, 82B44, 47H10.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Estamos interesados en una ecuación elíptica no homogénea con potencial aleatorio y no linealidad supercrítica. Obtenemos la existencia de solución casi seguramente para una clase de potenciales que incluye continuos y discretos. Además, proporcionamos una ley de grandes números para las soluciones obtenidas por conjuntos independientes y estimamos el valor esperado para sus normas L&#8734;.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Elliptic equations]]></kwd>
<kwd lng="en"><![CDATA[Random potentials]]></kwd>
<kwd lng="en"><![CDATA[Random nonlinear equations]]></kwd>
<kwd lng="es"><![CDATA[Ecuaciones elípticas]]></kwd>
<kwd lng="es"><![CDATA[potenciales aleatorios]]></kwd>
<kwd lng="es"><![CDATA[ecuaciones no lineales aleatorias]]></kwd>
</kwd-group>
</article-meta>
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