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Extended method of quasilinearization for a nonlinear three-point boundary value problem

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Języki publikacji
EN
Abstrakty
EN
In this paper, we discuss the generalized quasilinearization technique for a second order nonlinear differential equation with nonlinear three-point general boundary conditions. In fact, we obtain sequences of upper and lower solutions converging mono- tonically and quadratically to the unique solution of the nonlinear three-point boundary value problem.
Wydawca
Rocznik
Strony
803--814
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
autor
autor
  • Department of Mathematics Faculty of Science King Abdul Aziz University P.O. Box 80257 Jeddah 21589, Saudi Arabia, bashir_qua@yahoo.com
Bibliografia
  • [1] R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems, Amer. Elsevier, New York, 1965.
  • [2] V. Lakshmikantham, An extension of the method of quasilinearization, J. Optim. Theory Appl. 82 (1994), 315–321.
  • [3] V. Lakshmikantham, Further improvement of generalized quasilinearization, Nonlinear Anal. 27 (1996), 223–227.
  • [4] V. Lakshmikantham and A. S. Vatsala, Generalized Quasilinearization for Nonlinear Problems, Kluwer Academic Publishes, Dordrecht, 1998.
  • [5] J. J. Nieto, Generalized quasilinearization method for a second order differential equation with Dirichlet boundary conditions, Proc. Amer. Math. Soc. 125 (1997), 2599–2604.
  • [6] A. Cabada, J. J. Nieto and R. Pita-da-Veige, A note on rapid convergence of approximate solutions for an ordinary Dirichlet problem, Dynam. Contin. Discrete Impuls. Systems 4 (1998), 23–30.
  • [7] A. Cabada and J. J. Nieto, Quasilinearization and rate of convergence for higher order nonlinear periodic boundary value problems, J. Optim. Theory Appl. 108 (2001), 97–107.
  • [8] B. Ahmad, J. J. Nieto and N. Shahzad, The Bellman-Kalaba-Lakshmikantham quasilinearization method for Neumann problems, J. Math. Anal. Appl. 257 (2001), 356–363.
  • [9] B. Ahmad, J. J. Nieto and N. Shahzad, Generalized quasilinearization method for mixed boundary value problems, App. Math. Comput. 133 (2002), 423–429.
  • [10] B. Ahmad, A. Alsaedi and S. Sivasundaram, Approximation of the solution of nonlinear second order integro-differential equations, Dynamic Systems Appl. (to appear).
  • [11] W. Coppel, Disconjugacy, Lecture Notes in Mathematics, Vol. 220, Springer-Verlag, NewYork/Berlin, 1971.
  • [12] I. T. Kiguradze and A. G. Lomtatidze, On certain boundary value problems for second order linear ordinary differential equations with singularities, J. Math. Anal. Appl. 101 (1984), 325–347.
  • [13] C. P. Gupta, A second order m-point boundary value problem at resonance, Nonlinear Anal. 24 (1995), 1483–1489.
  • [14] C. P. Gupta and S. Trofimchuck, A priori estimates for the existence of a solution for a multi-point boundary value problem, J. Inequal. Appl. 5 (2000), 351–365.
  • [15] P. Eloe and Y. Gao, The method of quasilinearization and a three-point boundary value problem, J. Korean Math. Soc. 39 (2002) 319–330.
  • [16] B. Ahmad and T. G. Sogati, A second order three-point boundary value problem with mixed nonlinear boundary conditions, Methods Appl. Anal. 11 (2004), 295–302.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0018-0009
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