1. CJM 2003 (vol 55 pp. 724)
 Cao, Xifang; Kong, Qingkai; Wu, Hongyou; Zettl, Anton

SturmLiouville Problems Whose Leading Coefficient Function Changes Sign
For a given SturmLiouville equation whose leading coefficient
function changes sign, we establish inequalities among the eigenvalues
for any coupled selfadjoint boundary condition and those for two
corresponding separated selfadjoint boundary conditions. By a recent
result of Binding and Volkmer, the eigenvalues (unbounded from both
below and above) for a separated selfadjoint boundary condition can
be numbered in terms of the Pr\"ufer angle; and our inequalities can
then be used to index the eigenvalues for any coupled selfadjoint
boundary condition. Under this indexing scheme, we determine the
discontinuities of each eigenvalue as a function on the space of such
SturmLiouville problems, and its range as a function on the space of
selfadjoint boundary conditions. We also relate this indexing scheme
to the number of zeros of eigenfunctions. In addition, we
characterize the discontinuities of each eigenvalue under a different
indexing scheme.
Categories:34B24, 34C10, 34L05, 34L15, 34L20 

2. CJM 2000 (vol 52 pp. 248)
 Binding, Paul A.; Browne, Patrick J.; Watson, Bruce A.

Spectral Problems for NonLinear SturmLiouville Equations with Eigenparameter Dependent Boundary Conditions
The nonlinear SturmLiouville equation
$$
(py')' + qy = \lambda(1  f)ry \text{ on } [0,1]
$$
is considered subject to the boundary conditions
$$
(a_j\lambda + b_j) y(j) = (c_j\lambda + d_j) (py') (j), \quad j =
0,1.
$$
Here $a_0 = 0 = c_0$ and $p,r > 0$ and $q$ are functions depending
on the independent variable $x$ alone, while $f$ depends on $x$,
$y$ and $y'$. Results are given on existence and location of sets
of $(\lambda,y)$ bifurcating from the linearized eigenvalues, and
for which $y$ has prescribed oscillation count, and on completeness
of the $y$ in an appropriate sense.
Categories:34B24, 34C23, 34L30 
