THE ASYMPTOTIC BEHAVIOR OF THE GREEN FUNCTION OF THE BOUNDARY-VALUE PROBLEM FOR A SECOND-ORDER EQUATION ON A GEOMETRIC GRAPH

摘要

The boundary-value problem-u″(x) + su(x) = f(x), x∈T, u′∣ar = 0 (where s is a complex parameter with Res > 0) on an open connected geometric graph is considered. The asymptotic behavior as Im s → ∞ of the Green function is determined; it implies that the Green function has a preimage under the one-sided Laplace transform.