In this work we present the proof of a result due to Lars Hörmander which establishes a necessary condition for a linear operator with variable coefficients is globally resolvable.

The present work study the global solvability of first order real linear partial diferential operators when the principal part has precisely one equilibrium point. Moreover, examples and counterexamples are presented.

In this work, we introduce the wave front set WF,(u) of a classical distribution with respect to the ultradifferentiable classes of Beurling and Eomieu type. Our main goal is to present a detailed proof of the inclusion ...

In this work we study a reaction-difusion problem with nonlinear Neumann boundary condition. The objective is to present suficient conditions on the diffusion coeficient so that the problem has an stable nonconstant ...

In this dissertation we present a proof of a Bernard Malgrange theorem, which establishes a necessary and sufficient condition for the global solvability of a linear operator with constant coefficients.