Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 74, pp. 1-10.
Title: Sufficient conditions for functions to form Riesz bases
in $L_2$ and applications to nonlinear boundary-value problems
Author: Peter E. Zhidkov (Bogoliubov Lab. of Theoretical Physics, Dubna, Russia)
Abstract:
We find sufficient conditions for systems of functions to be
Riesz bases in $L_2(0,1)$. Then we improve a theorem
presented in [13] by showing that a ``standard'' system
of solutions of a nonlinear boundary-value problem, normalized
to 1, is a Riesz basis in $L_2(0,1)$.
The proofs in this article use Bari's theorem.
Submitted September 24, 2001. Published December 4, 2001
Math Subject Classifications: 41A58, 42C15, 34L10, 34L30.
Key Words: Riesz basis; infinite sequence of solutions;
nonlinear boundary-value problem.