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(1973)
Vvedenie v teoriyu uravnenii, vyrozhdayushchikhsya na granitse (Introduction to the Theory of Equations Degenerating on the Boundary), Novosibirsk: Novosibirsk
D.W. Bresters (1973)
On the Euler–Poisson–Darboux equationSIAM J. Math. Anal., 4
M. Sova (1966)
Cosine operator functions
A. Erdélyi (1970)
On the Euler-Poisson-Darboux equationJournal d’Analyse Mathématique, 23
J. Donaldson (1970)
A singular abstract cauchy problem.Proceedings of the National Academy of Sciences of the United States of America, 66 2
S.A. Tersenov (1973)
Vvedenie v teoriyu uravnenii, vyrozhdayushchikhsya na granitse (Introduction to the Theory of Equations Degenerating on the Boundary)
(1955)
Cauchy problem for systems of linear partial differential equations with Bessel - type differential operators
A. Baskakov, T. Katsaran, T. Smagina (2017)
Second-order linear differential equations in a Banach space and splitting operatorsRussian Mathematics, 61
H. Fattorini (1983)
A note on fractional derivatives of semigroups and cosine functionsPacific Journal of Mathematics, 109
A. Glushak (2006)
On the relationship between the integrated cosine function and the operator Bessel functionDifferential Equations, 42
A. Baskakov, L. Kabantsova, I. Kostrub, T. Smagina (2017)
Linear differential operators and operator matrices of the second orderDifferential Equations, 53
A. Glushak, O. Pokruchin (2016)
Criterion for the solvability of the cauchy problem for an abstract Euler–Poisson–Darboux equationDifferential Equations, 52
(1969)
Ordinary differential equations in linear topological space
A. Glushak (2017)
Abstract Cauchy problem for the Bessel–Struve equationDifferential Equations, 53
(2007)
Cauchy problem for an abstract Euler–Poisson–Darboux equation with the generator of an integrated cosine operator function, Nauchn
N.N. Lebedev (1963)
Spetsial’nye funktsii i ikh prilozheniya (Special Functions and Their Applications)
(1997)
Stabilization of a solution of the Dirichlet problem for an elliptic equation in a Banach space
A.V. Glushak, V.I. Kononenko, S.D. Shmulevich (1986)
A singular abstract Cauchy problemSov. Math., 30
(1974)
Integral’nye preobrazovaniya obobshchennykh funktsii (Integral Transformations of Generalized Functions)
A. Baskakov, A. Zagorskii (2007)
Spectral theory of linear relations on real Banach spacesMathematical Notes, 81
(1963)
Spetsial’nye funktsii i ikh prilozheniya (Special Functions and Their Applications), Moscow: Gos
In a Banach space E, we consider the abstract Euler–Poisson–Darboux equation u″(t) + kt −1 u′(t) = Au(t) on the half-line. (Here k ∈ ℝ is a parameter, and A is a closed linear operator with dense domain on E.) We obtain a necessary and sufficient condition for the solvability of the Cauchy problem u(0) = 0, lim t→0+ t k u′(t) = u 1, k < 0, for this equation. The condition is stated in terms of an estimate for the norms of the fractional power of the resolvent of A and its derivatives. We introduce the operator Bessel function with negative index and study its properties.
Differential Equations – Springer Journals
Published: Jun 11, 2018
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