En este texto se estudian, en primer lugar, algunos resultados sobre existencia, multiplicidad y no existencia de soluciones clásicas positivas para un problema elíptico semilineal. Para esto usamos técnicas sobre sub-supersoluciones desarrolladas por R. Shivaji y un resultado sobre semipositones debido a A. Castro, R. Shivaji y J. Garner.En segunda instancia se estudian algunos resultados sobre existencia, multiplicidad y no existencia de soluciones débiles positivas para un problema elíptico cuasi lineal que involucra el operador p-laplaciano. Para esto usamos métodos variacionales.
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