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Bargmann-Type Bounds

  • Juan Pablo Pinasco
Chapter
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Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter we study Bargmann-type bounds for the number of negative eigenvalues of Schrödinger equations, which is a well-known hypothesis for the nonoscillatory behavior of solutions of second-order problems on the half-line. Such bounds mean that there are no solutions with two zeros if \(\|xw(x)\|_{{L}^{1}}\) is smaller than a certain constant. We present some lower bounds for the first eigenvalue of linear and quasilinear problems involving integrals of the weights and some power of x, and we apply it to singular eigenvalue problems in unbounded intervals.

Keywords

Singular Eigenvalue Problems Quasilinear Problem Non-oscillatory Results Well-known Hypothesis Spectral Counting Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Juan Pablo Pinasco 2013

Authors and Affiliations

  • Juan Pablo Pinasco
    • 1
  1. 1.Departamento de MatematicaUniversidad de Buenos AiresBuenos AiresArgentina

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