Zhidkov, Peter E.2020-01-072020-01-072000-04-13Zhidkov, P. E. (2000). Basis properties of eigenfunctions of nonlinear Sturm-Liouville problems. <i>Electronic Journal of Differential Equations, 2000</i>(28), pp. 1-13.1072-6691https://hdl.handle.net/10877/9149We 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/yn} 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalRiesz basisNonlinear eigenvalue problemSturm-Liouville operatorCompletenessBasisArticle