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This article concerns an existence result for Floquet boundary value problems associated to semilinear differential inclusions with Carathéodory right hand side in a Hilbert space. We apply a continuation principle and we require a sharp (i.e., localized on the boundary) transversality condition. We give an application to a nonlinear partial differential inclusion with periodic conditions.
Wydawca
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Rocznik
Tom
Strony
237--258
Opis fizyczny
Bibliogr. 16 poz.
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autor
autor
autor
- Department of Engineering, University of Florence, Florence, Via S. Marta, 3, 50139 Firenze, Italy, Benedetti@math.unifi.it
Bibliografia
- [1] S. Aizicovici, N. S. Papageorgiou and V. Staicu, Periodic solutions of nonlinear evolution inclusions in Banach spaces, J. Nonlin. Convex Anal. 7 (2006), 163-177.
- [2] J. Andres and R. Bader, Asymptotic boundary value problems in Banach spaces, J. Math. Anal. Appl. 247 (2002), 437-457.
- [3] J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems. Kluwer, Dordrecht, 2003.
- [4] J. Andres, L. Malaguti and V. Taddei, Bounded solutions of Caratheodory differential inclusions: a bound sets approach, Abstr. Appl. Anal. 9 (2003), 547-571.
- [5] J. Andres, L. Malaguti and V. Taddei, A bounding function approach to multivalued boundary value problems, Dyn. Sist. Appl. 16 (2007), 37-48.
- [6] J. Andres, L. Malaguti and V. Taddei, On boundary value problems in Banach spaces, Dynam. Systems Appl. 18 (2009), 275-301.
- [7] J. L. Daleckii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces., Transl. Math. Monographs 43, Amer. Math. Soc, Providence, R.I., 1974.
- [8] Z. Ding and A. Kartsatos, Non-resonance problems for differential inclusions in separable Banach spaces. Proceed. Amer. Math. Soc. 124 (1996), 2357-2365.
- [9] R. G. Gaines and J. L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in mathematics, vol. 568, Springer Verlag, Berlin, 1977.
- [10] J. Garcfa-Falset, Existence results and asymptotic behavior for nonlocal abstract Cauchy problems, J. Math. Anal. Appl. 338 (2008), 639-652.
- [11] S. Hu and N. S. Papageorgiou, On the existence of periodic solutions for a class of nonlinear evolution inclusions. Boll. Un. Mat. Ital. B (7) 7 (1993) no. 3, 591-605.
- [12] M.I. Kamenskii, V. Obukhovskii and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Space. W. de Gruyter, Berlin, 2001.
- [13] J. Mawhin and H. B. Thompson, Periodic or bounded solutions of Caratheodory systems of ordinary differential equations, J. Dyn. Diff. Eq. 15, No. 2-3 (2003), 327-334.
- [14] V. Obukhovskii and P. Zecca, On boundary value problems for degenerate differential inclusions in Banach space, Abstr. Appl. Anal. 13 (2003), 769-784.
- [15] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, 1983.
- [16] X. Xue, Nonlocal nonlinear differential equations with a measure of noncompact-ness in Banach spaces, Nonlin. Anal. 70 (2009), 2593-2601.
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Bibliografia
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bwmeta1.element.baztech-article-LOD7-0033-0005