The deficiency indices of a symmetric third-order differential operator (Q1916647)

The deficiency indices of the minimal differential operator \(L_0\) generated in \(L^2 [0,\infty)\) by the differential expression \(ly = - 2iy''' + (p_1 (x) y')' - i(q_0 (x)y' + (q_0 (x) y)') + p_0 (x)y\), where \(p_0 (x)\), \(p_1 (x)\), \(q_0 (x) \in C^2\), are studied. The deficiency indices of \(L_0\) are studied under the assumption that all coefficients in \(ly\) equally contribute to the asymptotic behavior of the solutions of the equation \(ly = i \sigma y\), \(\sigma \neq 0\) as \(x \to \infty\). The asymptotic formulas for solutions of this equation are given and are used for finding the deficiency indices of \(L_0\).