The paper deals with the multivalued initial value problem x'(t) Є A(t, x)x+ F (t, x) for a.a. t in[a, b], x(a) = x_0 in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x and the investigation includes the case when both A and F have asuperlinear growth in x. We prove the existence of local and global classical solutions in the Sobolev space W1,p ([a, b], E) with 1 < p < ∞. Introducing a suitably defined Lyapunov-likefunction, we are able to investigate the topological structure of the solution set. Our main tool is a continuation principle in Frechét spaces and we prove the required pushingcondition in two different ways. Some examples complete the discussion.
Semilinear differential inclusions via weak topologies / I., Benedetti; Malaguti, Luisa; Taddei, Valentina. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 368:1(2010), pp. 90-102. [10.1016/j.jmaa.2010.03.002]
Semilinear differential inclusions via weak topologies
MALAGUTI, Luisa;TADDEI, Valentina
2010
Abstract
The paper deals with the multivalued initial value problem x'(t) Є A(t, x)x+ F (t, x) for a.a. t in[a, b], x(a) = x_0 in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x and the investigation includes the case when both A and F have asuperlinear growth in x. We prove the existence of local and global classical solutions in the Sobolev space W1,p ([a, b], E) with 1 < p < ∞. Introducing a suitably defined Lyapunov-likefunction, we are able to investigate the topological structure of the solution set. Our main tool is a continuation principle in Frechét spaces and we prove the required pushingcondition in two different ways. Some examples complete the discussion.File | Dimensione | Formato | |
---|---|---|---|
Benedetti Malaguti Taddei 2010.pdf
Accesso riservato
Tipologia:
Versione pubblicata dall'editore
Dimensione
438.59 kB
Formato
Adobe PDF
|
438.59 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris