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2004 | 24 | 1 | 73-96
Tytuł artykułu

On boundary value problems of second order differential inclusions

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents sufficient conditions for the existence of solutions to boundary-value problems of second order multi-valued differential inclusions. The existence of extremal solutions is also obtained under certain monotonicity conditions.
Twórcy
  • Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India
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, Dynamic Systems Appl. 12 (2003), 1-7.
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  • [3] J. Aubin and A. Cellina, Differential Inclusions, Springer Verlag 1984.
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  • [7] M. Benchohra, Upper and lower solutions method for second order differential inclusions, Dynam. Systems Appl. 11 (2002), 13-20.
  • [8] M. Benchohra and S.K. Ntouyas, On second order differential inclusions with periodic boundary conditions, Acta Math. Univ. Comenianea LXIX (2000), 173-181.
  • [9] M. Benchohra and S.K. Ntouyas, The lower and upper solutions method for first order differential inclusions with nonlinear boundary conditions, J. Ineq. Pure Appl. Math. 3 (1) (2002), Art. 14.
  • [10] B.C. Dhage, A functional integral inclusion involving discontinuities, Fixed Point Theory 5 (2004), 53-64.
  • [11] B.C. Dhage, A fixed point theorem for multi-valued mappings in Banach spaces with applications, Nonlinear Anal. (to appear).
  • [12] B.C. Dhage, Monotone method for discontinuous differential inclusions, Math. Sci. Res. J. 8 (3) (2004), 104-113.
  • [13] 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.
  • [14] B.C. Dhage and S. Heikkila, On nonlinear boundary value problems with deviating arguments and discontinuous right hand side, J. Appl. Math. Stoch. Anal. 6 (1993), 83-92.
  • [15] 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.
  • [16] B.C. Dhage and D.O. Regan, A lattice fixed point theorem and multi-valued differential equations, Functional Diff. Equations 9 (2002), 109-115.
  • [17] J. Dugundji and A. Granas, Fixed point theory, Springer Verlag 2003.
  • [18] N. Halidias and N. Papageorgiou, Second order multi-valued boundary value problems, Arch. Math. (Brno) 34 (1998), 267-284.
  • [19] S. Heikkila, On second order discontinuous scalar boundary value problem, Nonlinear Studies 3 (2) (1996), 153-162.
  • [20] S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker Inc., New York 1994.
  • [21] S. Heikkila, J.W. Mooney and S. Seikkila, Existence, uniqueness and comparison results for nonlinear boundary value problems involving deviating arguments, J. Diff. Eqn 41 (3) (1981), 320-232.
  • [22] 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.
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1053
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