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 \( y(0) = y(\tfrac{T} {2}) = 0 \).


Linear Space Null Space Force Term Finite Subset Fredholm Operator 
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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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