Sobre operadores íntegro-diferenciais e aplicações.

Abstract

In this work, we will study a class of integro-di erential operators. We will show some relevant results for the studied theory and we will apply, these results, in the study of problems involving the integro-di erential operator. Initially, we will show a maximum principle. We will use the maximun principle, to study the existence of a positive solution for Schrödinger-Poisson systems. Also, we will show an estimate for the weak solution of certain equations and we will use this estimate to study a class of equations of Schrödinger. We will present a abstract theorem and will use this theorem to study the existence of solution to Berestycki-Lions problems. Finally, we will present a Polya-Szegö type inequality for integro-di erential operators.