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En este artículo se presentan los resultados más importantes de mi trabajo de investigación en el estudio de la existencia, multiplicidad y propiedades cualitativas de las soluciones de problemas elípticos semilineales y cuasilineales.
Los teoremas que se presentan han sido obtenidos utilizando metodos variacionales, un principio de minimax demostrado por A. Castro, J. Cossio y J. M. Neuberger, teoría de grado, teoría de Morse y teoría de bifurcacion. Además se formulan una serie de preguntas abiertas relacionadas con los problemas en estudio, que esperamos sean de interés para los analistas no lineales. © Acad. Colomb. Cienc. Ex. Fis. Nat. 2016.
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