Lipschitz-continuity of the solution map of some nonconvex second-order differential inclusions

• Autorzy: Cernea A.
• Języki publikacji: EN

Abstrakty

EN

We prove the Lipschitz dependence on the initial condition of the solution set of a nonconvex second-order differential inclusions by applying the contraction principle in the space of selections of the multifunction instead of the space of solutions.

Słowa kluczowe

EN

cosine family of operators; fixed point; contractive set-valued map

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2009
• Tom: Nr 41
• Strony: 45--54
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Cernea A.

• Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14, Bucharest, Romania,

Bibliografia

• [1] Benchohra M., On second-order differential inclusions in Banach spaces, New Zealand J. Math., 30(2001), 5-13.
• [2] Benchohra M., Ntouyas S.K., Existence of mild solutions of second-order initial value problems for differential inclusions with nonlocal conditions, Atti. Sem. Mat. Fis. Univ. Modena, 49(2001), 351-361.
• [3] Castaing C., Valadier M., Convex analysis and measurable multifunctions, LNM 580, Springer, Berlin, 1977.
• [4] Cernea A., Some qualitative properties of the solution set of infinite horizon operational differential inclusions, Revue Roumaine Math. Pures Appl, 43(1998), 317-328.
• [5] Cernea A., On a second-order differential inclusion, submitted.
• [6] Covitz H., Nadler S.B. jr., Multivalued contraction mapping in generalized metric spaces, Israel J. Math., 8(1970), 5-11.
• [7] Dunford N., Pettis B.J., Linear operators and summable functions, Trans. Amer. Math. Soc., 47(1940), 323-392.
• [8] Fattorini O., Second-order linear differential equations in Banach spaces, Mathematical Studies vol. 108, North Holland, Amsterdam, 1985.
• [9] Heikkila S., Lakshmikantham V., Monotone iterative techniques for discontinuous nonlinear differential equations, Marcel Dekker, New York, 1994.
• [10] Kannai Z., Tallos P., Stability of solution sets of differential inclusions, Acta Sci. Math. (Szeged), 61(1995), 197-207.
• [11] Lim T.C., On fixed point stability for set valued contractive mappings with applications to generalized differential equations, J. Math. Anal. Appl., 110(1985), 436-441.
• [12] Talllos P., A Filippov-Gronwall type inequality in infinite dimensional space, Pure Math. Appl, 5(1994), 355-362.
• [13] Travis C.C., Webb G.F., Cosine families and abstract nonlinear second-order differential equations, Math. Hungarica, 32(1978), 75-96.