Limit circle criteria for 2nth order differential operators

Abstract

A formally self-adjoint differential operatorLis said to be of limit circle type at infinity if its highest order coefficient is zero-free and all solutionsxofL(x) = 0 are square-integrable on [a, ∞). (We will drop reference to “at infinity” in what follows.)For the second-order caseDunford and Schwartz (3) p. 1409 prove thatgiventhenLis of limit circle type if and only if