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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2008 • Question 4

Question

Math 6420 • PDE Fall 2008 • Question 4

On the interval \([0,1]\) use eigenfunctions to find the resolvent of the integral equation \[ u(x)-\lambda \int _0^1 x^2y^2u(y)\,dy=f(x). \] When does a solution not exist? Write down the pseudoresolvent in this case.

Raw LaTeX

On the interval \([0,1]\) use eigenfunctions to find the resolvent of the integral equation
\[
  u(x)-\lambda\int_0^1 x^2y^2u(y)\,dy=f(x).
\]
When does a solution not exist? Write down the pseudoresolvent in this case.

Topic Tags

Cauchy Integral Formula and Integral Theorems Distributions and Weak Solutions Linear Programming and Optimization Spectral Theory of Operators