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En este artículo se presentan los resultados más importantes de mi trabajo de investigación en el estudio de la existencia y de las propiedades de las soluciones de ecuaciones diferenciales parciales no lineales.
Donde λ ∈ R, Ω es un dominio acotado en RN con frontera suave, ∆ = n i=0 ∂/∂x2 i es el operador de Laplace y f : R → R es una función no lineal. Se presentan teoremas obtenidos utilizando teoría de bifurcación, métodos variacionales y un principio de minimax desarrollado por el autor en colaboración con A. Castro y J. M. Neuberger ([Cas-Cos-Nu1], 1997). Además, se incluyen algunos algoritmos para construir y visualizar soluciones a problemas no lineales del tipo (1) y una serie de preguntas abiertas.
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