- #1

joshmccraney

Gold Member

- 2,185

- 124

## Homework Statement

For a given ##a##, define $$B[u(x)] = u''(s) + \cos^2(a) u(s) - \frac{1}{2s_0}\int_{-s_0}^{s_0}(u''(s) + \cos^2(a) u(s) )\, ds,\\

s_0 = \frac{1}{\cos(a)}\arcsin(\cos a)$$

subject to boundary conditions

$$u'(s_0) + \cot (a) \cos (a) u(s_0) = 0\\

-u'(-s_0) + \cot (a) \cos (a) u(-s_0) = 0.$$

What is the Green's function associated with ##B[u(s)] = f## and it's boundary conditions?

## Homework Equations

Nothing comes to mind.

## The Attempt at a Solution

I attempted variation of parameters without considering the integral portion (which must be considered), but that technique failed: the two solutions I got from solving the ODE at ##-s_0## and ##+s_0## were linearly dependent, so their Wronskian was zero, and thus variation of parameters failed.

Does anyone have any idea how to solve this?