Density, Spectral Theory and Homoclinics for Singular Sturm-liouville Systems

We consider the singular system -(P(t)u')' + Q(t)u = lambda R(t)u. We give boundary conditions corresponding to the weak formulation, density results and conditions under which the set of eigenfunctions is total and orthogonal. Our results include the classical special functions. Finally, we apply these results to the problem on the real line: -(P(t>u')' + Q(t)u = V-u(t, u), t is an element of R, integral(R)[(Pu'.u') + (Qu.u)] < infinity, where V is superquadratic at infinity and subquadratic at the origin.