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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2014 • Question 4

Question

Math 6410 • ODE Fall 2014 • Question 4

Let \(p(t)>0\) be a smooth function that is periodic of least period \(T>0\). Show that every solution approaches zero as \(t\to \infty \). \[ x''+p(t)x'+x=0 \]

Raw LaTeX

Let \(p(t)>0\) be a smooth function that is periodic of least period \(T>0\). Show
that every solution approaches zero as \(t\to\infty\).
\[
  x''+p(t)x'+x=0
\]

Topic Tags

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