Variational Methods

Period of duration of course
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Course info
Number of course hours
40
Number of hours of lecturers of reference
40
Number of hours of supplementary teaching
0
CFU 6
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Type of exam

Oral exam and seminars

Lecturer

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Prerequisites

It is recommended familiarity with Functional Analysis, theory of Elliptic Equations and with basic notions in topology.

Programme

- basic review of calculus in Banach spaces

- continuity and differentiability of Nemitski’s operators

- free and constrained critical points - the Palais-Smale condition and the deformation lemma

- the Mountain-Pass theorem and other variational schemes

- Lusternik-Schnirelman’s category - Krasnoselski’s genus

- existence of infinitely-many solutions for even unbounded functionals

- Allen-Cahn functional and minimal surfaces

Educational aims

The aim of the course is to show the combination of topology and analysis techniques to solve nonlinear elliptic equations with variational structure. 

Bibliographical references

- Ambrosetti-Malchiodi: Nonlinear Analysis and Semilinear Elliptic Problems, C.U.P., 2007

- Ambrosetti-Prodi: A primer of Nonlinear Analysis, C.U.P., 1993

- Struwe: Variational Methods, Springer, 2008