Equações integrais envolvendo operadores de dispersão não-local.

Abstract

In this work, we will study two integral equations involving a non-local dispersion operator that arises from the study of reaction-diffusion equations. We will use Nonlinear Functional Analysis methods to determine solutions for these problems. More precisely, in the first problem we will use the Bifurcation Method to show the existence of a positive solution, while in the second problem we will use Sub-Super Solution Methods and the degree for γ-condensing applications, which is an extension of the degree of Leray-Schauder for a larger class of identity perturbations, to obtain an Ambrosetti-Prodi result.