 |
|
Spectral Problems for Non-Linear Sturm-Liouville Equations with Eigenparameter Dependent Boundary Conditions |
Canad. J. Math. 52(2000), 248-264
Published:2000-04-01
Printed: Apr 2000
Printed: Apr 2000
- Paul A. Binding
- Patrick J. Browne
- Bruce A. Watson
Abstract
The nonlinear Sturm-Liouville 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.
| MSC Classifications: |
34B24 - Sturm-Liouville theory [See also 34Lxx] 34C23 - Bifurcation [See also 37Gxx] 34L30 - Nonlinear ordinary differential operators |