Geodesic
Sufficient conditions for functions to form Riesz bases in \(L_2\) and applications to nonlinear boundary-value problems
Electronic journal of differential equations, Tome 2001 (2001)
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.
Classification : 41A58, 42C15, 34L10, 34L30
Keywords: Riesz basis, infinite sequence of solutions, nonlinear boundary-value problem 
@article{EJDE_2001__2001__a193,
     author = {Zhidkov,  Peter E.},
     title = {Sufficient conditions for functions to form {Riesz} bases in {\(L_2\)} and applications to nonlinear boundary-value problems},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {1009.34077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a193/}
}
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%0 Journal Article
%A Zhidkov,  Peter E.
%T Sufficient conditions for functions to form Riesz bases in \(L_2\) and applications to nonlinear boundary-value problems
%J Electronic journal of differential equations
%D 2001
%V 2001
%U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a193/
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%F EJDE_2001__2001__a193
Zhidkov,  Peter E. Sufficient conditions for functions to form Riesz bases in \(L_2\) and applications to nonlinear boundary-value problems. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a193/