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2006 | 26 | 1 | 57-76
Tytuł artykułu

The method of upper and lower solutions for perturbed nth order differential inclusions

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Języki publikacji
EN
Abstrakty
EN
In this paper, an existence theorem for nth order perturbed differential inclusion is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions on the multi-functions involved in the inclusion. Our results extend the existence results of Dhage et al. [7,8] and Agarwal et al. [1].
Twórcy
  • Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India
  • Department of Applied Mathematics, Babeş-Bolyai University Cluj-Napoca, Kogălniceanu 1, 3400 Cluj-Napoca, Romania
Bibliografia
  • [1] R. Agarwal, B.C. Dhage and D. O'Regan, The upper and lower solution method for differential inclusions via a lattice fixed point theorem, Dynam. Systems Appl. 12 (2003), 1-7.
  • [2] J. Aubin and A. Cellina, Differential Inclusions, Springer Verlag 1984.
  • [3] M. Benchohra, Upper and lower solutions method for second order differential inclusions, Dynam. Systems Appl. 11 (2002), 13-20.
  • [4] B.C. Dhage, A fixed point theorem for multi-valued mappings with applications, preprint.
  • [5] B.C. Dhage, Multi-valued mappings and fixed points I.
  • [6] B.C. Dhage and S.M. Kang, Upper and lower solutions method for first order discontinuous differential inclusions, Math. Sci. Res. J. 6 (2002), 527-533.
  • [7] B.C. Dhage, T.L. Holambe and S.K. Ntouyas, Upper and lower solutions method for second order discontinuous differential inclusions, Math. Sci. Res. J. 7 (2003), 206-212.
  • [8] B.C. Dhage, T.L. Holambe and S.K. Ntouyas, The method of upper and lower solutions for Caratheodory nth order differential inclusions, Electronic J. Diff. Equ. 8 (2004), 1-9.
  • [9] N. Halidias and N. Papageorgiou, Second order multi-valued boundary value problems, Arch. Math. Brno 34 (1998), 267-284.
  • [10] S. Heikkila and V. Lakshmikantham, Monotone Iterative Technique for Nonlinear Discontinuous Differential Equations, Marcel Dekker Inc., New York 1994.
  • [11] S. Hu and N. Papageorgiu, Handbook of Multi-valued Analysis, Volume I, Kluwer Academic Publishers, Dordrecht 1997.
  • [12] A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
  • [13] M. Martelli, A Rothe's type theorem for non compact acyclic-valued maps, Boll. Un. Mat. Ital. 4 (Suppl. Fasc.) (1975), 70-76.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1064
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