GENERALIZED LIOUVILLE PROPERTY FOR SCHR?ODINGER OPERATOR ON GRAPHS
Commun. Korean Math. Soc. 2005 Vol. 20, No. 3, 521-529
Printed July 1, 2005
Seok Woo Kim and Yong Hah Lee
Konkuk University, Ewha Womans University
Abstract : We prove that the dimension of the space of positive (bounded, respectively) solutions for the Schr?odinger operator whose potential q is nonnegative on a graph with q-regular ends is equal to the number of ends (q-nonparabolic ends, respectively).
Keywords : Liouville property, Schrodinger operator, q-regular end.
MSC numbers : 31C05, 31C20
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