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On Oscillation Properties of Self-Adjoint Boundary Value Problems of Fourth Order

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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… Click to show full abstract

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: self adjoint; adjoint boundary; fourth order; boundary value; value problems

Journal Title: Doklady Mathematics
Year Published: 2021

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