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I would like to obtain the Green function for the operator F, F [u(x)] = u '''', and the boundary conditions u(0) = u'(0) = u (1) = u' (1) = 0.

I am looking for a function G ( x, s ) such that G'''' (x,s) = delta (x-s) (the apecis referring to differentiation w.r.t. x, and delta referring to Dirac's function).

All I managed to do is the following:

1) solve the ode for x other than s, u = a +b*x + c * x^2 +d * x^3

2) considering the first two B.C. for x < s, and the other two for x > s I get some conditions for the constants in terms of linear equations

3) an additional equation could be written to impose continuity at s

But then? What other conditions are avaialbe to determine the missing constants?

Thanks as usual

Muzialis

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# Green function for Euler beam

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