{"id":38680,"date":"1998-08-10T00:00:00","date_gmt":"1998-08-10T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/metodos-topologicos-y-variaciones-en-el-estudio-de-problemas-de-contorno-resonantes-con-no-linealidades-periodicas\/"},"modified":"1998-08-10T00:00:00","modified_gmt":"1998-08-10T00:00:00","slug":"metodos-topologicos-y-variaciones-en-el-estudio-de-problemas-de-contorno-resonantes-con-no-linealidades-periodicas","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/metodos-topologicos-y-variaciones-en-el-estudio-de-problemas-de-contorno-resonantes-con-no-linealidades-periodicas\/","title":{"rendered":"Metodos topologicos y variaciones en el estudio de problemas de contorno resonantes con no linealidades periodicas."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Francisco Roca Rodriguez <\/strong><\/h2>\n<p>Utilizando m\u00e9todos topol\u00f3gicos y variacionales probamos la existencia de soluciones, as\u00ed como ciertas propiedades cualitativas de las mismas, de una clase de ecuaciones diferenciales no lineales de segundo orden con condiciones de frontera de tipo dirichlet y no-linealidad t-peri\u00f3dica. Se describe el rango de ciertos operadores que determina el conjunto de soluciones de la correspondiente ecuaci\u00f3n. Varias cuestiones que permanec\u00edan abiertas, planteadas por prestigiosos matem\u00e1ticos de la talla internacional de solinini, ward, dancer y otros, son parcial o totalmente resueltas en la presente tesis.  en la primera parte se aborda la ecuaci\u00f3n diferencial ordinaria utilizando de manera novedosa una combinaci\u00f3n del m\u00e9todo alternativa (o reducci\u00f3n de liapunov-schmidt) sub y supersoluciones y el estudio de la topolog\u00eda de ciertos subconjuntos.  m\u00e1s adelante se analiza en profundidad la geometr\u00eda del funcional de euler, lo que da propiedades adicionales sobre la estructura del conjunto de puntos cr\u00edticos y de m\u00ednimo global.  la \u00faltima parte est\u00e1 dedicada al estudio del correspondiente problema de ecuaciones en derivadas parciales. Con el empleo, principalmente, del teorema de los multiplicadores de lagrange en dimensi\u00f3n infinita, se generalizan algunos resultados a una dimensi\u00f3n superior.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Metodos topologicos y variaciones en el estudio de problemas de contorno resonantes con no linealidades periodicas.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Metodos topologicos y variaciones en el estudio de problemas de contorno resonantes con no linealidades periodicas. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Francisco Roca Rodriguez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Granada<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 08\/10\/1998<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Antonio Ca\u00f1ada Villar<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: jean Mawhim <\/li>\n<li>Juan  Jos\u00e9 Nieto rolg (vocal)<\/li>\n<li>jaume Llibre salo (vocal)<\/li>\n<li>pavel Drabek (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Francisco Roca Rodriguez Utilizando m\u00e9todos topol\u00f3gicos y variacionales probamos la existencia de soluciones, as\u00ed como ciertas propiedades [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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