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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2018 • Question 6

Question

Math 6410 • ODE Fall 2018 • Question 6

Consider Newton’s equation \[ \ddot {x}+\frac {x}{2+x^2}=\epsilon \cos t \] Prove that there is an \(\epsilon _0>0\) such that if \(\abs {\epsilon }<\epsilon _0\) then there is a \(2\pi \)-periodic solution.

Raw LaTeX

Consider Newton's equation
\[
  \ddot{x}+\frac{x}{2+x^2}=\epsilon\cos t
\]
Prove that there is an \(\epsilon_0>0\) such that if \(\abs{\epsilon}<\epsilon_0\)
then there is a \(2\pi\)-periodic solution.

Topic Tags

Distributions and Weak Solutions Entropy Solutions, Shocks, and Rarefactions Periodic Orbits, Limit Cycles, and Orbital Stability Poincare Maps and Periodic Solutions