Convergence of eigenfunction expansions corresponding to nonlinear Sturm-Liouville operators

Abstract

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.

Keywords

• Sturm-Liouville operator
• basis property
• eigenfunction.