The paper deals with a semilinear evolution equation in a reflexive and separable Banach space. The non-linear term is multivalued, upper Caratheodory and it depends on a retarded argument. The existence of global almost exact, i.e. classical, solutions is investigated. The results are based on a continuation principle for condensing multifields and the required transversalities derive from the introduction of suitable generalized guiding functions. As a consequence, the equation has a bounded globally viable set. The results are new also in the lack of retard and in the single valued case. A brief discussion of a non-local diffusion model completes this investigation.
Guiding-like functions for semilinear evolution equations with retarded nonlinearities / S., Cecchini; Malaguti, Luisa. - In: ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS. - ISSN 1417-3875. - ELETTRONICO. - 87:87(2012), pp. 1-24. [10.14232/ejqtde.2012.1.87]
Guiding-like functions for semilinear evolution equations with retarded nonlinearities
MALAGUTI, Luisa
2012
Abstract
The paper deals with a semilinear evolution equation in a reflexive and separable Banach space. The non-linear term is multivalued, upper Caratheodory and it depends on a retarded argument. The existence of global almost exact, i.e. classical, solutions is investigated. The results are based on a continuation principle for condensing multifields and the required transversalities derive from the introduction of suitable generalized guiding functions. As a consequence, the equation has a bounded globally viable set. The results are new also in the lack of retard and in the single valued case. A brief discussion of a non-local diffusion model completes this investigation.File | Dimensione | Formato | |
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