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First Order Differential Equations (Continued)

  • V. Lakshmikantham
  • A. S. Vatsala
Part of the Mathematics and Its Applications book series (MAIA, volume 440)

Abstract

Having discussed a variety of results relative to IVPs of scalar differential equation so far in chapter 1, we shall now embark to investigate, in Section 2.1, periodic boundary value problems (PBVPs) in the framework of generalized quasilinearization. We prove some typical results of interest to avoid monotony. Anti-periodic BVPs are the contents of Section 2.2, which require new ideas compared to PBVP’s, since similar generalization is no longer valid. Section 2.3 deals with interval analysis approach to the method of generalized quasilinearization, where one can compute arbitrary sharp bounds in terms of interval valued functions. This has significance in large computations.

Keywords

Unique Solution Nonlinear Problem Interval Function Order Differential Equation Lower Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • V. Lakshmikantham
    • 1
  • A. S. Vatsala
    • 2
  1. 1.Florida Institute of TechnologyDivision of Applied MathematicsMelbourneUSA
  2. 2.College of Sciences, Department of MathematicsUniversity of Southwestern LouisianaLafayetteUSA

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