On the extension problem for singular accretive differential operators (Q1076319)

Let the differential expression \(\tau y=\frac{1}{\omega}\sum^{n}_{j=0}(-1)^ n(P_{n- j}y^{(j)})^{(j)}\) be singular on an interval I and have real coefficients with \(\omega >0\), \(p_ 0\neq 0\) a.e. and \(\omega\), \(1/p_ 0,p_ 1,...,p_ n\) locally integrable on I. Suppose also that the Dirichlet integral \(\sum^{n}_{j=0}\int_{I}P_{n-j}| y^{(j)}|^ 2\) is a norm on the maximal domain defined by \(\tau\) and that \(\tau\) satisfies the strong limit-point condition at each singular end point of I. Under these conditions the minimal operator \(T_ 0\) generated by \(\tau\) in \(L^ 2(I)\) is an accretive operator (in fact a positive symmetric operator). In this paper a complete description of all the maximal accretive extensions of \(T_ 0\) is obtained, these extensions being given in terms of explicit boundary conditions. The paper is a sequel to [\textit{W. D. Evans} and \textit{I. Knowles}, J. Funct. Anal. 63, 276-298 (1985; Zbl 0578.47037)] which dealt with the regular problem.