Regularization of two-term differential equations with singular coefficients by quasiderivatives

Abstract

We propose a regularization of the formal differential expression l(y)=i my (m)(t)+q(t)y(t), t ∈(a,b), of order m ≥ 3 by quasiderivatives. It is assumed that the distribution coefficient q has the antiderivative Q ∈ L([a,b];ℂ). In the symmetric case (Q = Q̄),we describe self-adjoint and maximal dissipative/accumulative extensions of the minimal operator and its generalized resolvents. In the general (nonself-adjoint) case, we establish the conditions of convergence for the resolvents of the analyzed operators in norm. The case where m = 2 and Q ∈ L 2 ([a,b];ℂ) was studied earlier. © 2012 Springer Science+Business Media, Inc.