Example 9.11.46659B6A5D3749

Example 9.11.46.659B6A5D3749 Without the assumption $\Psi =0$, a nonconstant $k$ does not force a nonconstant solution. Take $\Psi =\log 2$ and $k(s)=2/(2-s)^{n+1}$. Then $s=2x/(1+x)$, $\ell =\log (1+x)$ and

Thus $\nu =\beta ^ n$. Since $\frac{\mathrm{d}}{\mathrm{d} s}(s/(2-s))^ n=nk(s)s^{n-1}$, one has $I=1/n$, $M=d$ and $c_ b=1$. The formulas (9.11.42) give $R=1/(2-s)$ and $Q(s)=\log (2-s)$, hence $U=\log 2$. The normalized solution is zero, although $k$ is nonconstant.