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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generalized quasilinearization method for a second order ordinary differential equation with Dirichlet boundary conditions
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by Juan J. Nieto PDF
Proc. Amer. Math. Soc. 125 (1997), 2599-2604 Request permission

Abstract:

We study the existence and approximation of solutions for a nonlinear second order ordinary differential equation with Dirichlet boundary value conditions. We present a generalized quasilinearization technique to obtain a sequence of approximate solutions converging quadratically to a solution.
References
  • R. Bellman, Methods of Nonlinear Analysis, Vol. II. Academic Press, New York, 1973.
  • Richard E. Bellman and Robert E. Kalaba, Quasilinearization and nonlinear boundary-value problems, Modern Analytic and Computational Methods in Science and Mathematics, Vol. 3, American Elsevier Publishing Co., Inc., New York, 1965. MR 0178571
  • G. S. Ladde, V. Lakshmikantham, and A. S. Vatsala, Monotone iterative techniques for nonlinear differential equations, Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics, vol. 27, Pitman (Advanced Publishing Program), Boston, MA; distributed by John Wiley & Sons, Inc., New York, 1985. MR 855240
  • V. Lakshmikantham, An extension of the method of quasilinearization, J. Optim. Theory Appl. 82 (1994), no. 2, 315–321. MR 1286689, DOI 10.1007/BF02191856
  • V. Lakshmikantham and S. Malek, Generalized quasilinearization, Nonlinear World 1 (1994), no. 1, 59–63. MR 1282859
  • V. Lakshmikantham and J. J. Nieto, Generalized quasilinearization for nonlinear first order ordinary differential equations, Nonlinear Times Digest 2 (1995), no. 1, 1–9. MR 1333329
  • V. Lakshmikantham, N. Shahzad and J. J. Nieto, Methods of Generalized Quasilinearization for Periodic Boundary Value Problems, Nonlinear Anal. 27 (1996), 143–151.
  • Juan J. Nieto and Alberto Cabada, A generalized upper and lower solutions method for nonlinear second order ordinary differential equations, J. Appl. Math. Stochastic Anal. 5 (1992), no. 2, 157–165. MR 1214298, DOI 10.1155/S1048953392000133
  • N. Shahzad and S. Sivasundaram, Further generalization of quasilinearization method for boundary value problems, Nonlinear Times Digest 2 (1995), no. 1, 59–67. MR 1333334
  • N. Shahzad and A. S. Vatsala, Improved generalized quasilinearization method for second order boundary value problem, Dynam. Systems Appl. 4 (1995), no. 1, 79–85. MR 1312481
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Additional Information
  • Juan J. Nieto
  • Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Spain
  • Email: amnieto@usc.es
  • Received by editor(s): March 13, 1996
  • Additional Notes: The author’s research was partially supported by D.G.I.C.Y.T. (Spain), project PB94-0610, and by EC Network, CHRX-CT94-0555
  • Communicated by: Hal L. Smith
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2599-2604
  • MSC (1991): Primary 34A45, 34B15
  • DOI: https://doi.org/10.1090/S0002-9939-97-03976-2
  • MathSciNet review: 1402880