ΕΘΝΙΚΟ ΚΑΙ ΚΑΠΟΔΙΣΤΡΙΑΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΑΘΗΝΩΝ
ΤΜΗΜΑ
ΜΑΘΗΜΑΤΙΚΩΝ
Τ ΟΜΕ ΑΣ ΣΤ ΑΤ Ι ΣΤ Ι ΚΗ Σ Κ ΑΙ ΕΠΙ ΧΕΙΡ Η ΣΙ ΑΚ ΗΣ ΕΡ ΕΥ Ν ΑΣ
ΠΑΝΕΠΙΣΤΗΜΙΟΠΟΛΗ ΑΘΗΝΑ 15784
TEL +30210-7276-382, FAX +30210-7276-381
Αθήνα, 17 Μαΐου 2005
Ομιλία Γενικού Σεμιναρίου
Ομιλητής: Καθηγητής Athanasios G. Kartsatos
Πανεπιστήμιο South Florida, Tampa, Florida, (Η.Π.Α.)
Τίτλος:
Topological Degree Theories and Eigenvalue Problems
in Banach Spaces
Ημερομηνία:
Παρασκευή 20 Μαΐου 2005, ώρα 13:00 – 14:00
Τόπος:
Αίθουσα Γ23
Περίληψη
Let X be a real reflexive Banach space with dual X * . We assume that X and X *
have been renormed so that they both are locally uniformly convex. Let
*
T : X  D(T )  2 X be maximal monotone and C : (0, Λ]  G  X * (G open,
bounded  X ) demicontinuous, bounded and of type (S  ) w.r.t. x. We seek an
eigenvalue λ  (0, Λ] and an eigenvector x  D(T )  G such that Tx  C ( λ, x)  0 .
We use the Browder and Skrypnik degree theories, for perturbations of maximal
monotone operators, as well as the degree theory by Skrypnik and the author for
densely defined perturbations of densely defined maximal monotone operators. The
current theory makes use of approximate problems of the type
Tt x  C ( λ, x)  εJx  0 ,
ε  0 , where J : X  X * is the duality mapping of X, and Tt : X  X * is defined by
Tt  (T 1  tJ 1 ) 1 , t  0 . It is shown that such pairs of operators T, C, exist naturally
in the field of partial differential equations.