Higher Analysis

The main aim of the course is to provide the students with an enlargement of their knowledge about ordinary differential equations. The main guidelines are: generalized solutions for the Cauchy problem related to first order differential equations in Banach spaces; variational formulations of two-point boundary value problems for second order differential equations. Also, it will be stimulated the student ability of applying the knowledgement and understanding of the constructed theory to specific problems.

1. Bounded variation functions. Absolutely continuous functions.

2. Differential and integral calculus in Banach spaces.

3. Ordinary differential equations in Banach spaces.

4. Variational formulations of two-point boundary value problems for second order equations.

1. E. Hille - R. S. Phillips, Functional analysis and semi-groups, American Mathematical Society, 1957.

2. E. Hewitt - K. Stromberg, Real and abstract analysis, Springer, 1975.

3. H. Brézis, Analisi funzionale, Liguori Editore, 1995.