P. E. Zhidkov
We consider three nonlinear eigenvalue problems that consist of
with one of the following boundary conditions:
where p is a positive constant. Under smoothness and monotonicity conditions on f, we show the existence and uniqueness of a sequence of eigenvalues and corresponding eigenfunctions such that has precisely n roots in the interval (0,1), where n=0,1,2,....
For the first boundary condition, we show that is a basis and that is a Riesz basis in the space . For the second and third boundary conditions, we show that is a Riesz basis.
Submitted November 17, 1999. Published April 13, 2000.
Math Subject Classifications: 34L10, 34L30, 34L99.
Key Words: Riesz basis, nonlinear eigenvalue problem, Sturm-Liouville operator, completeness, basis.
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| Peter E. Zhidkov |
Bogoliubov Laboratory of Theoretical Physics
Joint Institute for Nuclear Research
141980 Dubna (Moscow region), Russia
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