  Recent solar neutrino results together with the assumption of a stationary
Sun imply severe constraints on the individual components of the total neutrino
flux : $\Phi_{Be} \leq 0.7 \cdot 10^{9} cm^{-2} s^{-1}, \Phi_{CNO} \leq 0.6
\cdot 10^{9} cm^{-2} s^{-1}$ and $64 \cdot 10^{9} cm^{-2} s^{-1} \leq
\Phi_{pp+pep} \leq 65 \cdot 10^{9} cm^{-2} s^{-1}$ (at 1$ \sigma$ level), the
constraint on $\nu_{Be}$ being in strong disagreement with $\Phi_{Be}^{SSM} = 5
\cdot 10^{9} cm^{-2} s^{-1}$. We study a large variety of non-standard solar
models with low inner temperatures, finding that the temperature profiles T(m)
follow the homology relationship: T(m)=k$T(m)^{SSM}$, so that they are
specified just by the central temperature $T_{c}$. There is no value of $T_{c}$
which can account for all the available experimental results and also if we
restrict to consider just Gallium and Kamiokande results the fit is poor.
Finally we discuss what can be learned from new generation experiments, planned
for the detection of monochromatic solar neutrinos, about the properties of
neutrinos and of the Sun.
