Two-point b.v.p. for multivalued equations with weakly regular r.h.s. |
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Authors: | Irene Benedetti |
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Institution: | a Department of Mathematics and Informatics, University of Perugia, I-06123, Italyb Department of Engineering Sciences and Methods, University of Modena and Reggio Emilia, I-42122, Italyc Department of Pure and Applied Mathematics, University of Modena and Reggio Emilia, I-41125, Italy |
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Abstract: | A two-point boundary value problem associated to a semilinear multivalued evolution equation is investigated, in reflexive and separable Banach spaces. To this aim, an original method is proposed based on the use of weak topologies and on a suitable continuation principle in Fréchet spaces. Lyapunov-like functions are introduced, for proving the required transversality condition. The linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one. Some applications are given, to the study of periodic and Floquet boundary value problems of partial integro-differential equations and inclusions appearing in dispersal population models. Comparisons are included, with recent related achievements. |
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Keywords: | primary 34G25 secondary 34B15 34A60 |
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