Comparison of eigenvalues for lidstone boundary value problems on a measure chain

The theory of u(0)-positive operators with respect to a cone in a Banach sp ace is applied to the class of even-order differential equation on measure chains [GRAPHICS] satisfying the lidstone boundary conditions x(Delta 2i)(0) = 0, 0 less than or equal to i less than or equal to m - 1; x(Delta 2j) (sigma(2)(1)) = 0, 0 less than or equal to j less than or equal to m - i. The existence of a s mallest positive eigenvalue is obtained and then a theorem is established c omparing the smallest positive eigenvalues for two problems of this type. ( C) 1999 Elsevier Science Ltd. All rights reserved.