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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 2019 • Question 4

Question

Math 6410 • ODE Fall 2019 • Question 4

Under what conditions on the parameters \(a\) and \(b\) does the boundary value problem \[ u''+u=\sin (x),\qquad u(0)=a,\qquad u(\pi )=b, \tag {5} \] have a solution? Is the solution, if it exists, unique? If not, why not?

Raw LaTeX

Under what conditions on the parameters \(a\) and \(b\) does the boundary value problem
\[
  u''+u=\sin(x),\qquad u(0)=a,\qquad u(\pi)=b,
  \tag{5}
\]
have a solution? Is the solution, if it exists, unique? If not, why not?

Topic Tags

Boundary Value Problems Boundary Value Problems and Sturm-Liouville Theory Distributions and Weak Solutions Poincare Maps and Periodic Solutions