Inequalities Among Eigenvalues Of Sturm-Liouville Problem With Periodic Coefficients

For h-periodic coefficients it is well known that eigenvalues of some self-adjoint complex boundary conditions on an interval of length h are periodic eigenvalues on intervals of length kh for k>2.We identify which of the un-countable number of complex conditions produces periodic and semi-periodic eigenvalues on the larger intervals.In addition,we prove an analogous result for semi-periodic eigenvalues.Furthermore,we give an 1-1 correspondence between these eigenvalues.