Geodesic
On oscillation properties of self-adjoint boundary value problems of fourth order
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 10-15.

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The connection between the number of internal zeros of nontrivial solutions to fourth-order self-adjoint boundary value problems and the inertia index of these problems is studied. We specify the types of problems for which such a connection can be established. In addition, we specify the types of problems for which a connection between the inertia index and the number of internal zeros of the derivatives of nontrivial solutions can be established. Examples demonstrating the effectiveness of the proposed new approach to an oscillatory problem are considered.
Keywords: boundary value problems for ordinary differential equations, spectral and oscillatory problems, inertia index, Kellogg kernels. 
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     author = {A. A. Vladimirov and A. A. Shkalikov},
     title = {On oscillation properties of self-adjoint boundary value problems of fourth order},
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A. A. Vladimirov; A. A. Shkalikov. On oscillation properties of self-adjoint boundary value problems of fourth order. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 496 (2021), pp. 10-15. http://geodesic.mathdoc.fr/item/DANMA_2021_496_a1/

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