Regularization of two-term differential equations with singular coefficients by quasiderivatives - Goryunov, A. S.; Mikhailets, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
We propose a regularization of the formal differential expression$$l(y) = i^m y^{(m)}(t) + q(t)y(t),\; t \in (a, b),$$of order $m ≥ 3$ by using quasiderivatives. It is assumed that the distribution coefficient $q$ has an antiderivative $Q \in L ([a, b]; \mathbb{C})$. In the symmetric case $(Q = \overline{Q})$, we describe self-adjoint and maximal dissipative/accumulativeextensions of the minimal operator and its generalized resolvents. In the general (nonselfadjoint)case, we establish conditions for the convergence of the resolvents of the considered operators innorm.The case where $m = 2$ and $Q \in L_2 ([a, b]; \mathbb{C})$ was studied earlier.