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

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Ukrainian Mathematical Journal Aims and scope

We propose a regularization of the formal differential expression

$$ l(y) = {i^m}{y^{(m)}}(t) + q(t)y(t),\quad t \in \left( {a,\,b} \right), $$

of order m ≥ 3 by quasiderivatives. It is assumed that the distribution coefficient q has the antiderivative \( Q \in L\left( {\left[ {a,\,b} \right];\mathbb{C}} \right) \). In the symmetric case \( \left( {Q = \bar{Q}} \right) \) 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 \( Q \in {L_2}\left( {\left[ {a,\,b} \right];\mathbb{C}} \right) \) was studied earlier.

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  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    A. S. Goryunov & V. A. Mikhailets

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  1. A. S. Goryunov
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  2. V. A. Mikhailets
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 9, pp. 1190–1205, September, 2011.

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Goryunov, A.S., Mikhailets, V.A. Regularization of two-term differential equations with singular coefficients by quasiderivatives. Ukr Math J 63, 1361–1378 (2012). https://doi.org/10.1007/s11253-012-0584-6

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  • DOI: https://doi.org/10.1007/s11253-012-0584-6

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