Keywords: D'Alembertian, homotopy argument, eigenvalues.
2]-[DELTA] is the D'Alembertian, h is a given function in [L.
k+1] [member of] [sigma]() are two consecutive eigenvalues of the D'Alembertian and [sigma]() is the spectrum of the D'Alembertian.
1) has been studied by Mustonen and Berkovits in  and , and by Brezis and Nirenberg in  but only for N = 1 and when g(x, t, s)/s is located strictly between two consecutive eigenvalues of the D'Alembertian, more precisely when [[lambda].
is the restriction of the D'Alembertian operator on Im() = (D()) and D() is the domain of the D'Alembertian operator.
If there exist two positive Consecutive eigenvalues of the D'Alembertian [[lambda].
Dirac's master wave equation can be factorized--essentially by taking the square-root of the d'Alembertian
operator applied to a Majorana 2-spinor wavefunction--to obtain not only Dirac's famous electron equation (in the common 4-spinor formalism), but also the equations for more exotic spinning particles (including the Proca equation, the Duffin-Kemmer equation for spins 0 and 1, and the Rarita-Schwinger equations for spin 3/2).