BooksecrCollected Volumepp. 55–70

On a class of Schrödinger operators exhibiting spectral transition

  • Diana Barseghyan

    University of Ostrava, Czech Republic
  • Olga Rossi

    University of Ostrava, Czech Republic
On a class of Schrödinger operators exhibiting spectral transition cover
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Abstract

We show that the operator for λ<π24\lambda<\frac{\pi^2}{4} is bounded from below and has purely discrete spectrum, while for λ>π24\lambda>\frac{\pi^2}{4} its spectrum contains the real line. In the critical case λ=π24\lambda=\frac{\pi^2}{4} we prove that the spectrum coincides with the half line [0,)[0, \infty).