Semilinear differential inclusions via weak topologies
| Autor: | Valentina Taddei, Luisa Malaguti, Irene Benedetti |
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| Rok vydání: | 2010 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics Applied Mathematics Mathematical analysis Eberlein–Šmulian theorem Banach space Banach manifold Semilinear differential inclusions in Banach spaces Compact operators Continuation principles Pushing condition semilinear differential inclusions in Banach spaces Compact operator Separable space compact operators continuation principles pushing condition Sobolev space Besov space Interpolation space Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 368:90-102 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2010.03.002 |
| Popis: | The paper deals with the multivalued initial value problem x ′ ∈ A ( t , x ) x + F ( t , x ) for a.a. t ∈ [ 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 a superlinear growth in x . We prove the existence of local and global classical solutions in the Sobolev space W 1 , p ( [ a , b ] , E ) with 1 p ∞ . Introducing a suitably defined Lyapunov-like function, we are able to investigate the topological structure of the solution set. Our main tool is a continuation principle in Frechet spaces and we prove the required pushing condition in two different ways. Some examples complete the discussion. |
| Databáze: | OpenAIRE |
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