A. Goriunov

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Articles: 2

Multi-interval Sturm-Liouville problems with distributional coefficients

Andrii Goriunov

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 26 (2020), no. 2, 103-110

The paper investigates spectral properties of multi-interval Sturm-Liouville operators with distributional coefficients. Constructive descriptions of all self-adjoint and maximal dissipative/accumulative extensions and also all generalized resolvents in terms of boundary conditions are given.

Regularization of singular Sturm-Liouville equations

Andrii Goriunov, Vladimir Mikhailets

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 16 (2010), no. 2, 120-130

The paper deals with the singular Sturm-Liouville expressions $$l(y) = -(py')' + qy$$ with the coefficients $$q = Q', \quad 1/p, Q/p, Q^2/p \in L_1, $$ where the derivative of the function $Q$ is understood in the sense of distributions. Due to a new regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent approximation is investigated and all self-adjoint and maximal dissipative extensions and generalized resolvents are described in terms of homogeneous boundary conditions of the canonical form.


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