Variational and topological methods for partial differential equation

• Grant number: 13/21563-3
• Support Opportunities: Regular Research Grants
• Start date: December 01, 2013
• End date: November 30, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gaetano Siciliano
• Grantee: Gaetano Siciliano
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Our research project is based on some problems which are described in terms of partial differential equations; many problems in physics or geometry can be described by differential equations.Some examples of the equations we want to study, are related with the Schroedinger equation and Klein-Gordon (possibly coupled with the Maxwell equations), or some problems involving non-local differential equations or related with some fields of differential geometry (e.g, harmonic maps, constant mean curvature surfaces, geodesics).These are classical themes and very studied in these last years, although they need to be better investigated.In particular we are interested in critical point theory to find solutions of variational partial differential equations. Moreover these equations could be quasilinear, and also a nonlocal term can be present.The aim s to study existence, multiplicity of solutions, as well as solutions of ground states, their symmetries or bifurcation phenomena associated. (AU)