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Lyapunov-type inequalities for third-order linear differential equations under the non-conjugate boundary conditions. (English) Zbl 1400.34029

Summary: In this paper, we obtain the best constant in the Lyapunov-type inequality for third-order linear differential equations under the non-conjugate boundary conditions by bounding the Green function of the same problem. In this direction, to the best of our knowledge, there is no paper dealing with Lyapunov-type inequalities for the non-conjugate boundary value problems. By using such inequalities, we obtain sharp lower bounds for the eigenvalues of corresponding equations.

MSC:

34B05 Linear boundary value problems for ordinary differential equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34B27 Green’s functions for ordinary differential equations
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