The Forced Pendulum

Robert F. Brown

Chapter Chapter 5 in A Topological Introduction to Nonlinear Analysis, 2014, pp 33-42 from Springer

Abstract: 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 Chap. 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: Dirichlet Boundary Condition; Force Term; Homogeneous Equation; Fixed Point Theory; Compactness Property (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-11794-2_5

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