The paper deals with a multivalued initial value problem in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous and the investigation includes the case when both the linear part A and the nonlinear part F have a superlinear growth. We prove the existence of local and global classical solutions. When introducing a suitably defined Lyapunov-like function, we are able to investigate the topological structure of the solution set. Some examples complete the discussion.
Semilinear differential inclusions via weak topologies
BENEDETTI, Irene;
2010
Abstract
The paper deals with a multivalued initial value problem in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous and the investigation includes the case when both the linear part A and the nonlinear part F have a superlinear growth. We prove the existence of local and global classical solutions. When introducing a suitably defined Lyapunov-like function, we are able to investigate the topological structure of the solution set. Some examples complete the discussion.File in questo prodotto:
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