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Abstract

The rest of Part I will be devoted to demonstrating the usefulness of two of the tools we have developed: the Schauder fixed point theorem and a compactness property of C k -spaces that is a consequence of the Ascoli-Arzela theorem. We used information from the Ascoli-Arzela and Schauder theories in Chapter 1, to prove the Cauchy-Peano theorem by topological methods. In this chapter, we will illustrate the use of these tools by showing how they establish the existence of solutions to a differential equation problem that comes up in the study of the pendulum.

Keywords

Periodic Solution Dirichlet Boundary Dirichlet Boundary Condition Force Term Homogeneous Equation 
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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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Robert F. Brown
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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