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 inclusionsappearing in dispersal population models. Comparisons are included, with recent related achievements.

Two-point b.v.p. for multivalued equations with weakly regular r.h.s / I., Benedetti; Malaguti, Luisa; Taddei, Valentina. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 74:(2011), pp. 3657-3670. [10.1016/j.na.2011.02.046]

Two-point b.v.p. for multivalued equations with weakly regular r.h.s.

MALAGUTI, Luisa;TADDEI, Valentina
2011

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 inclusionsappearing in dispersal population models. Comparisons are included, with recent related achievements.
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Two-point b.v.p. for multivalued equations with weakly regular r.h.s / I., Benedetti; Malaguti, Luisa; Taddei, Valentina. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 74:(2011), pp. 3657-3670. [10.1016/j.na.2011.02.046]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/649481
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