Electron. J. Diff. Eqns., Vol. 2004(2004), No. 87, pp. 1-10.

Convergence of eigenfunction expansions corresponding to nonlinear Sturm-Liouville operators

Alexander S. Makin, H. Bevan Thompson

It is well known that the classical linear Sturm-Liouville eigenvalue problem is self-adjoint and possesses a family of eigenfunctions which form an orthonormal basis for the space L_2. A natural question is to ask if a similar result holds for nonlinear problems. In the present paper, we examine the basis property for eigenfunctions of nonlinear Sturm-Liouville equations subject to general linear, separated boundary conditions.

Submitted October 10, 2003. Published June 29, 2004.
Math Subject Classifications: 34L10, 34B15.
Key Words: Sturm-Liouville operator; basis property; eigenfunction.

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Alexander S. Makin
Moscow State Academy of Instrument-Making and Informatics
Stromynka 20, 107846, Moscow, Russia
email: alexmakin@yandex.ru
H. Bevan Thompson
Department of Mathematics, The University of Queensland
Queensland 4072, Australia
email: hbt@maths.uq.edu.au

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