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Abstract

In Chapter 5 we saw that if e: RR is an odd, T-periodic function, then the forced pendulum equation with forcing term e, that is,
$$ y'' + a \sin y = e, $$
always has a solution y: RR that is also an odd, T-periodic function. Remember how we constructed that solution: we built it up out of copies of a solution \( y:[0,\tfrac{T} {2}] \to R \) to the Dirichlet boundary value problem corresponding to that differential equation, that is, with the boundary condition \( y(0) = y(\tfrac{T} {2}) = 0 \).

Keywords

Linear Space Null Space Force Term Finite Subset Fredholm Operator 
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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