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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · ODE, PDE & Applied Mathematics › Ordinary Differential Equations

“Every boundary value problem has a Green's function” — false

Counterexample: y″ + π²y = f on [0,1] with y(0) = y(1) = 0

$λ = π^{2}$ is an eigenvalue of the homogeneous problem, so the operator is not invertible and no Green's function exists.

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