Nonlinear Differencial Equations

Abstract

The research done by the various members of the present project cover central areas in the theory of Nonlinear Differential Equations. The problems studied have an intrinsic importance in Mathematics itself, as well a broad range of applicability to other branches of Science. For that matter, one observes that they are object of attention and work in many excellent schools around the world. All the lines of research presented here are connected among themselves. For instance, elliptic equations represent steady states of evolution equations. In this way, these two large classes of equations meet in the study of asymptotic behavior of the solutions of the latter. In modelling problems coming from the applications, conditions inherent to the phenomena imply in the choice of the type of equation to be considered (hyperbolic, parabolic, eliptic) as well as in the type boundary conditions and initial conditions (Cauchy problem, Dirichlet problem, Neumann problem, mixed problems, equations with delay...). As soon as the spatial variable in the problem ins on-dimensional, the qualitative theory of ordinary differential equations becomes relevant. A detailed analysis of this project and of the 'Resumé"(in particular, the list of publications) show that the members of this project have covered with success the several aspects of this rich area of Mathematics. The researchers and their collaborators, members of the present project, are actively involved in research and possess and effective interaction with other mathematicians from universities in Brazil and abroad. The importance of the present projetct resides in the wish of an intensification of scientific exchange between UNICAMP and USP-SC, which are institutions having mathematicians working in close areas. The unity of the present project can be seen from the analysis of the methodology used, where the techniques belong to the same branches of Mathematics: Functional Analysis, Nolinear Analysis, Topological Methods, Fixed Point Theorems, Compact Operators, Monotone Operators. (AU)