Desigualdades do tipo trudinger-moser e existência de soluções para equações elípticas em R2

Abstract

In this work we will approach a class of inequalities of the Trudinger-Moser type in subspaces of radial functions with logarithmic weights defined in the unit ball of R2. As an application of these inequalities, using the Lagrange Multipliers Theorem, we will prove the existence of solutions for a class of non-homogeneous elliptic equations involving nonlinearity with subcritical exponential growth of the Trudinger-Moser type. Later, still using variational methods, we will study elliptic problems involving subcritical nonlinear terms, defined in whole space R2.