Mathematics

General objective : The main purpose of the course is to give the student a good knowledge of the basic topics in Nonlinear Analysis which are important in the study of Differential Equations. Specific objectives : Knowledge and understanding: at the end of the course the student will have learned the basic theory to study differential problems with a variational structure, in particular those involving semilinear elliptic equations. Applications : at the end of the course the student will be able to solve simple problems which require the use of variational methods to study critical points of nonlinear functionals. Critical abilities: the student will have the basic knowledge of the variational theory of Differential Equations. He/she will be able to choose the appropriate methods to study nonlinear differential problems. Communication skills: the student will have the ability to expose the topics studied in the oral exam. Learning skills: the student will be capable to face the study of nonlinear variational problems which arise in the field of Differential Equations so that he/she can continue the study of more advanced topics.