A criterion for correct solvability in Lp(R) of a general Sturm-Liouville equation

We consider an 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) for p is an element of (1, infinity) with the following conditions: r > 0, q >= 0, 1/r is an element of L-1(loc) (R), q is an element of L-1(loc) (R), integral(0)(-infinity) dt/r(t)=integral(infinity)(0) dt/r(t)=infinity. By a solution of the above-mentioned equations, we mean any function y that is absolutely continuous together with ry' and satisfies it almost everywhere on R. Under the above-mentioned conditions, we give a criterion for the correct solvability of the above-mentioned equation in L-p(R) for p is an element of (1, infinity).