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On Higher-Order Differential Operators with Singularity inside the Interval
Mathematical Notes, 2002Differential equations with singularities inside the interval arise in different areas of mathematics and in applications. A wide class of differential equations with turning points can be reduced to the equations considered by the author. This paper is concerned with the non-selfadjoint boundary value problem for the studied differential equation with
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Spectral analysis of higher order differential operators with unbounded coefficients
Mathematische Nachrichten, 2011AbstractHigher even order linear differential operators with unbounded coefficients are studied. For these operators the eigenvalues of the characteristic polynomials fall into distinct classes or clusters. Consequently the spectral properties, deficiency indices and spectra, of the underlying differential operators are superpositions of the ...
Behncke, Horst +1 more
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On higher-order differential operators with a singular point
Inverse Problems, 1993The paper is concerned with a very specific inverse spectral problem. This problem is formulated as follows: Given the Weyl matrix \({\mathfrak M}(\lambda)\), construct a differential operator \(l\) associated with the higher-order differential equation \[ ly\equiv y^{(n)}+ \sum^{n- 2}_{j=0} \left({\nu_ j\over x^{n-j}}+ q_ j(x)\right) y^{(j)}=\lambda y\
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Higher-order Differential Operators in $$L^p$$
2014In previous sections we have found conditions for the \(L^p\)-dissipativity of secondorder scalar equations and systems. One can ask whether these results hold for higher-order operators. In this chapter it is proved that the answer is negative.
Alberto Cialdea, Vladimir Maz’ya
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On higher-order differential operators with a regular singularity
Sbornik: Mathematics, 1995Summary: A boundary-value problem for the non-self-adjoint differential operators \[ \ell y \equiv y^{(n)} + \sum^{n - 2}_{j = 0} \left( {\nu_j \over x^{n - j}} + q_j(x) \right) y^{(j)}, \quad 0 < x < T, \] with a regular singularity at zero is investigated.
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SPECTRAL THEORY OF HIGHER ORDER DIFFERENTIAL OPERATORS
Proceedings of the London Mathematical Society, 2005The absolutely continuous spectrum of a very general class of differential operators of order $2n$ is determined, for operators whose coefficients satisfy conditions that combine smoothness and decay properties. The main methods are asymptotic integration and the analysis of the associated $M$-matrix.
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Regularized traces of higher-order singular differential operators
Mathematical Notes, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kozko, A. I., Pechentsov, A. S.
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Properties of one higher order matrix-differential operator
Russian Universities Reports. Mathematics, 2022The article considers a linear matrix-differential operator of the n-th order of the form A^n. For it and for the operator (A ̃^(-1) )^n, an analytical expression is derived, for which an operator analog of the Newton binomial is obtained. A lemma on the solution of a linear equation is given.
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Polynomial approximations of solutions of higher-order operator-differential equations
Ukrainian Mathematical Journal, 1994Summary: The Cauchy problem for higher-order differential-operator equations is considered in a Banach space. A polynomial approximation is constructed.
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Integro-Differential Equation with a Higher-Order Two-Dimensional Whitham Operator
Journal of Mathematical Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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