GREEN-LIOUVILLE APPROXIMATION AND CORRECT SOLVABILITY IN Lp(R) OF THE GENERAL STURM-LIOUVILLE EQUATION

We consider the equation -(r(x)y '(x))' + q(x)y(x) = f(x), x is an element of R, where f is an element of L-p(R), p is an element of (1, infinity) and r > 0, 1/r is an element of L-1(loc)(R), q is an element of L-1(loc)(R). For particular equations of this form, we suggest some methods for the study of the question on requirements to the functions r and q under which the above equation is correctly solvable in the space L-p(R), p is an element of(1, infinity).