A variational principle for the Landau equation

The Landau equation describing the collective modes of an infinite many-fermion system is cast into a form which displays explicitly its structure as a homogeneous Fredholm equation of the second kind with non-symmetric kernel. A variational principle appropriate to this equation is constructed by noting the analogy to the integral form of the Schrödinger equation. The Landau equation is also re-expressed in terms of two coupled equations with symmetric kernels.