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. <i>Electronic Journal of Differential Equations, 2000</i>(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 |