Desigualdade de Díaz-Saá e aplicações - Cunha, Lucas Gabriel Ferreira da (2017)
In this work we will present and demonstrate the Diaz & Saá’s Inequality thus like the tools used in their demonstration and we will apply the results obtained in semilinear elliptic problems with limited and not limited domains. We will present necessary and sufficient conditions to show the existence and uniqueness of solution for the following −Δp u = f (x, u) problem type in a limited domain. Moreover, we will also obtain regularity of solution to this problem. Next we will show results relative to the first eigenvalue of a (p, q) − Laplacian system type in R^N .