# Basis Properties of Eigenfunctions of Nonlinear Sturm-Liouville Problems

 dc.contributor.author Zhidkov, Peter E. dc.date.accessioned 2020-01-07T18:06:24Z dc.date.available 2020-01-07T18:06:24Z dc.date.issued 2000-04-13 dc.description.abstract We consider three nonlinear eigenvalue problems that consist of -y'' + ƒ(y2)y = λy with one of the following boundary conditions: y(0) = y(1) = 0 y'(0) = p, y'(0) = y(1) = 0 y(0) = p, y'(0) = y'(1) = 0 y(0) = p, where p is a positive constant. Under smoothness and monotonicity conditions on ƒ, we show the existence and uniqueness of a sequence of eigen-values {λn} and corresponding eigenfunctions {yn} such that yn(x) has precisely n roots in the interval (0,1), where n = 0, 1, 2,.... For the first boundary condition, we show that {yn} is a basis and that {yn/ dc.description.abstract yn dc.description.abstract } is a Riesz basis in the space L2(0, 1). For the second and third boundary conditions, we show that {yn} is a Riesz basis. dc.description.department Mathematics dc.format Text dc.format.extent 13 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Zhidkov, P. E. (2000). Basis properties of eigenfunctions of nonlinear Sturm-Liouville problems. Electronic Journal of Differential Equations, 2000(28), pp. 1-13. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/9149 dc.language.iso en dc.publisher Southwest Texas State University, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas. dc.subject Riesz basis dc.subject Nonlinear eigenvalue problem dc.subject Sturm-Liouville operator dc.subject Completeness dc.subject Basis dc.title Basis Properties of Eigenfunctions of Nonlinear Sturm-Liouville Problems dc.type Article

## Files

### Original bundle

Now showing 1 - 1 of 1
Name:
2000-Zhidkov.pdf
Size:
156.69 KB
Format:
Description: