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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Spring 2014 • Question 3

Question

Math 6410 • ODE Spring 2014 • Question 3

Show that for small \(\norm {\epsilon }\), there is a \(2\pi \)-periodic solution to the forced Duffing’s equation \[ \ddot {y}+3y+\epsilon y^3=\cos t. \]

Raw LaTeX

Show that for small \(\norm{\epsilon}\), there is a \(2\pi\)-periodic solution to the
forced Duffing's equation
\[
  \ddot{y}+3y+\epsilon y^3=\cos t.
\]

Topic Tags

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