Abstract:
We obtain asymptotic representations as λ→∞ in the upper and lower half-planes for the solutions of the Sturm–Liouville equation
−y″+p(x)y′+q(x)y=λ2ρ(x)y,x∈[a,b]⊂R,
under the condition that q is a distribution of first-order singularity, ρ is a positive absolutely continuous function, and p belongs to the space L2[a,b].
Keywords:
Sturm–Liouville equation, asymptotic solution, singular coefficient, Volterra integral operator, fundamental system of solutions, space of bounded functions.
Citation:
V. E. Vladikina, A. A. Shkalikov, “Asymptotics of the Solutions of the Sturm–Liouville Equation with Singular Coefficients”, Mat. Zametki, 98:6 (2015), 832–841; Math. Notes, 98:6 (2015), 891–899
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\paper Asymptotics of the Solutions of the Sturm--Liouville Equation with Singular Coefficients
\jour Mat. Zametki
\yr 2015
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\issue 6
\pages 832--841
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\jour Math. Notes
\yr 2015
\vol 98
\issue 6
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Linking options:
https://www.mathnet.ru/eng/mzm10976
https://doi.org/10.4213/mzm10976
https://www.mathnet.ru/eng/mzm/v98/i6/p832
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M. B. Zvereva, “The Problem of Deformations of a Singular String with a Nonlinear Boundary Condition”, Lobachevskii J Math, 45:1 (2024), 555
Alibek Yeskermessuly, Trends in Mathematics, 4, Modern Problems in PDEs and Applications, 2024, 175
A. P. Kosarev, A. A. Shkalikov, “Asymptotic representations of solutions of $n\times n$ systems of ordinary differential equations with a large parameter”, Math. Notes, 116:2 (2024), 283–302
Michael Ruzhansky, Alibek Yeskermessuly, “Heat equation for Sturm–Liouville operator with singular propagation and potential”, Journal of Applied Analysis, 2024
M. Yu. Vatolkin, “To the Study of Various Representations of Solutions of Quasi-Differential Equations in the Form of Sums of Series and Some of Their Applications”, Comput. Math. and Math. Phys., 64:11 (2024), 2571
M. Yu. Vatolkin, “On the spectrum of a quasidifferential boundary value problem of the second order”, Russian Math. (Iz. VUZ), 67:1 (2023), 1–19
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Natalia P. Bondarenko, “Regularization and Inverse Spectral Problems for Differential Operators with Distribution Coefficients”, Mathematics, 11:16 (2023), 3455
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Kamenskii M. Fitte Paul Raynaud de Wong N.-Ch. Zvereva M., “A Model of Deformations of a Discontinuous Stieltjes String With a Nonlinear Boundary Condition”, J. Nonlinear Var. Anal., 5:5 (2021), 737–759
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V. E. Vladykina, “Asymptotics of fundamental solutions to Sturm–Liouville problem with respect to spectral parameter”, Moscow University Mathematics Bulletin, 74:1 (2019), 38–41
V. E. Vladykina, “Spectral characteristics of the Sturm–Liouville operator under minimal restrictions on smoothness of coefficients”, Moscow University Mathematics Bulletin, 74:6 (2019), 235–240
M. Kamenskii, Ch.-F. Wen, M. Zvereva, “Oscillations of the string with singuliarities”, J. Nonlinear Convex Anal., 20:8, SI (2019), 1525–1545
M. V. Ruzhansky, N. E. Tokmagambetov, “On a Very Weak Solution of the Wave Equation for a Hamiltonian in a Singular Electromagnetic Field”, Math. Notes, 103:5 (2018), 856–858
N. F. Valeev, O. V. Myakinova, Ya. T. Sultanaev, “On the Asymptotics of Solutions of a Singular $n$th-Order Differential Equation with Nonregular Coefficients”, Math. Notes, 104:4 (2018), 606–611
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