Criteria for correct solvability of a general Sturm–Liouville equation in the space L₁(R)

We consider the equation -(r(x)y′(x))′+q(x)y(x)=f(x),x∈Rwhere f∈ L₁(R) and r>0,q≥0,1/r∈L1loc(R),q∈L1loc(R),lim|d|→∞∫x-dxdtr(t)·∫x-dxq(t)dt=∞.By a solution of (1), we mean any function y, absolutely continuous in R together with ry^′, which satisfies (1) almost everywhere in R. Under conditions (2) and (3), we give a criterion for correct solvability of (1) in the space L₁(R).