Accumulation of complex eigenvalues of indefinite Sturm-Liouville operators

Behrndt, Jussi GND; Katatbeh, Qutaibeh; Trunk, Carsten GND

Spectral properties of singular Sturm-Liouville operators of the form A = sgn ()(− d2 dx2 + V ) with the indefinite weight x 7→ sgn (x) on R are studied. For a class of potentials with lim|x|!1 V (x) = 0 the accumulation of complex and real eigenvalues of A to zero is investigated and explicit eigenvalue problems are solved numerically.

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