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Seminari di equazioni differenziali e applicazioni: High multiplicity for superlinear indefinite problems

Lunedì 21 Ottobre 2013, ore 16:15 - Aula 2BC30 - Andrea Tellini

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Lunedì 21 Ottobre 2013 alle ore 16:15 in aula 2BC30, Andrea Tellini (Universidad Complutense de Madrid) terrà un seminario dal titolo "High multiplicity for superlinear indefinite problems".

Abstract
In this talk I will present a multiplicity result for positive solutions of a class of superlinear indefinite differential equations which arise in population dynamics to model the behavior of a species in a polluted habitat where competitive and cooperative effects among the individuals are combined. Using the amplitude of the cooperative effect as a parameter, and applying some techniques which are more related to ODEs, we have been able to describe the structure of the solutions' set in a one dimensional case, which is rather complex due to the high number of the solutions that the problem can admit.
The multiplicity in higher spatial dimensions, as well as the linear stability of the solutions will be also discussed in full generality, using in this case genuine PDEs techniques.
Finally, I will present some numerical experiments, both for cases already treated analytically and new ones.
The content of the talk is based on joint works with J. Lopez-Gomez (Universidad Complutense de Madrid), M. Molina-Meyer (Universidad Carlos III de Madrid) and F. Zanolin (Universita' degli Studi di Udine).

Rif. Int.
M. Bardi, C. Marchi, L. Rossi.

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