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In this paper we consider the problem of obtaining upper bounds for the positive bound states associated with the Schrödinger operators with long range potentials. We have extended the size of the class of long range potentials for which one can establish the nonexistence of positive eigenvalues, improving upon the recent results of G. B. Khosrovshahi, H. A. Levine and L. E. Payne (Trans. Amer. Math. Soc. 253 (1979), 211-228).

On the absence of positive eigenvalues of Schrödinger operators with long range potentials