On a computer assisted proof of the existence of eigenvalues below the essential spectrum of the Sturm-Liouville problem

[摘要] There is considerable interest in determining the existence of eigenvalues of the Sturm-Liouville problem -(py')' + qy = lambda wy, where the independent variable x is an element of [0, infinity) and p,q and w are real-valued functions, and lambda is the spectral parameter. In general, an analytic attack on this problem is quite difficult and usually requires the use of the Variational principal together with choice of suitable test functions. We show how results from functional analysis together with interval analysis and interval arithmetic can be used, not only to determine the existence of such eigenvalues, but also to compute provably correct bounds on their values. (C) 2000 Elsevier Science B.V. All rights reserved.

[发布日期] 2000-12-15