Abstract
We establish the attainability of the infimum m γ for the minimal eigenvalues of the boundary-value problems
as the nonnegative potential q ∈ L 1[0, 1] ranges over the unit sphere of the space L γ[0, 1], where γ ∈ (0, 1). We also establish that, for γ ≤ 1 − 2π −2, the equality m γ holds and that, otherwise, the inequality m γ is valid.
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Original Russian Text © A. A. Vladimirov, E. S. Karulina, 2015, published in Matematicheskie Zametki, 2015, Vol. 97, No. 6, pp. 832–840.
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Vladimirov, A.A., Karulina, E.S. A priori lower bound for the minimal eigenvalue of a Sturm-Liouville problem with boundary conditions of the second type. Math Notes 97, 846–853 (2015). https://doi.org/10.1134/S000143461505020X
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DOI: https://doi.org/10.1134/S000143461505020X