The Sturm Liouville Problems with a random variable in Boundary Conditions

Abstract

We discussed the Sturm-Liouville problems with random variableξn involving in bound-ary conditions which represent a support coefficient for elastic rope. We have aconclusion that if the random variable in the boundary condition have convergence property, then the eigenvalues will also have a similar convergence property. We also give an asymptotic formula to approximate the large eigenvalues. This formula give an asymptotic relationship between eigenvalues and the support coefficient ξn when the eigenvalues are very large.