Quadratic Singular Perturbation Problems

  • K. W. Chang
  • F. A. Howes
Part of the Applied Mathematical Sciences book series (AMS, volume 56)

Abstract

In this chapter we investigate the asymptotic behavior of solutions of boundary value problems for the differential equation
$$\varepsilon y''{\text{ = p}}\left( {{\text{t}},{\text{y}}} \right){{\text{y'}}^{\text{2}}}{\text{ + g}}\left( {{\text{t}},{\text{y}}} \right),{\text{a}} < {\text{t}} < {\text{b}}$$
(DE)
The novelty here is the presence of the quadratic term in y’. The more general differential equation
$$\varepsilon y''{\text{ = p}}\left( {{\text{t}},{\text{y}}} \right){{\text{y'}}^{\text{2}}}{\text{ + f}}\left( {{\text{t}},{\text{y}}} \right){\text{y' + g}}\left( {{\text{t}},{\text{y}}} \right)$$
will not be studied, since it can be reduced to the form (DE) in some cases by the familiar device of completing the square. Our decision to study the simpler equation (DE) rather than the more general equation stems from a desire to present representative results for this “quadratic” class of problems without having to deal with extra complexities in notation.

Keywords

uRea Vasil 

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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • K. W. Chang
    • 1
  • F. A. Howes
    • 2
  1. 1.Department of MathematicsUniversity of CalgaryCalgaryCanada
  2. 2.Department of MathematicsUniversity of CaliforniaDavisUSA

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