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Derived from
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20410756 AM420 - PARTIAL DIFFERENTIAL EQUATIONS in Mathematics LM-40 BATTAGLIA LUCA, BESSI UGO
(syllabus)
Calculus in Banach spaces, derivation, Implicit Function Theorem;
Bifurcation theorem, Ljapunov-Schmidt method;
Energy-minimizing solutions, coercivity, lower semi-continuity;
Saddle point solutions, Mountain Pass Theorem;
Topological degree, Linking Theorems;
Ljusternik-Schnirelmann Category, existence of infinitely many solutions.
(reference books)
A. Ambrosetti, A. Malchiodi - "Nonlinear Analysis and Semilinear Elliptic Problem" - Cambridge
P. Rabinowitz - "Minimax methods in critical point theory with application to differential equations" - American Mathematical Society
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Università Roma Tre