Electron. J. Diff. Eqns., Vol. 2001(2001), No. 74, pp. 1-10.

Sufficient conditions for functions to form Riesz bases in L_2 and applications to nonlinear boundary-value problems

Peter E. Zhidkov

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.

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Peter E. Zhidkov
Bogoliubov Laboratory of Theoretical Physics,
Joint Institute for Nuclear Research,
141980 Dubna (Moscow region), Russia
e-mail: zhidkov@thsun1.jinr.ru

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