II.

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II. $\lambda = 0.$

The general solution for (1.2) is

$\begin{displaymath} G(x) = C_1 x + C_2 \end{displaymath}$

The boundary conditions

$\begin{displaymath} G(0) = 0,\;\; G(L) = 0 \end{displaymath}$

imply that

$\begin{displaymath} C_2 = 0 \mbox{ follows from } G(0)=0 \end{displaymath}$

and

$\begin{displaymath} C_1 L = 0 \mbox{ follows from } G(L) = 0 \end{displaymath}$

Hence, the only possible solution is

and

Sergey Nikitin 2004-10-25