Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Winter 2004 • Question 5

Question

Math 6410 • ODE Winter 2004 • Question 5

Periodic Coefficients. Prove that if \(\lvert \epsilon \rvert \ne 0\) is small enough, then all solutions are bounded \[ \ddot {u}+[1+\epsilon \sin (3t)]u=0. \] [Convert to a system of equations. Give a condition for the boundedness of all solutions. Verify that the condition is satisfied in this case.]

Raw LaTeX

\textbf{Periodic Coefficients.}
Prove that if \(\lvert\epsilon\rvert\ne0\) is small enough, then all solutions are bounded
\[
  \ddot{u}+[1+\epsilon\sin(3t)]u=0.
\]
[Convert to a system of equations. Give a condition for the boundedness of all solutions.
Verify that the condition is satisfied in this case.]

Topic Tags

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