Abramov, A. A.; Yukno, L. F. A method for solving a nonlinear self-adjoint spectral problem for a second order ordinary differential equation with nonlocal boundary conditions. (English. Russian original) Zbl 0947.65093 Differ. Equations 35, No. 2, 205-210 (1999); translation from Differ. Uravn. 35, No. 2, 206-211 (1999). The nonlinear eigenvalue problem for the second order ordinary differential equation on the interval \([0,T]\) with nonlocal boundary conditions depending on the spectral parameter is considered. Using the results of A. A. Abramov [Zh. Vychisl. Mat. Mat. Fiz. 6, 819-831 (1991; Zbl 0742.65067)] and using the notion of points conjugate to the right and left endpoints, the authors propose a method of evaluating the number of eigenvalues (with regards to their multiplicities) lying in a given closed interval without finding the eigenvalues themselves. Moreover a method of finding an eigenvalue with prescribed number as well as a method for computing the number of a given eigenvalue are considered. Some results of numerical experiments are presented. A computation is done for the equation \(y''+g(t,\lambda)=0\) with the periodic boundary conditions for different functions \(q(t,\lambda)\). Reviewer: T.Regińska (Warszawa) MSC: 65L15 Numerical solution of eigenvalue problems involving ordinary differential equations 34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators Keywords:nonlinear self adjoint spectral problem; nonlocal boundary conditions; number of eigenvalues; approximation of eigenvalues; nonlinear eigenvalue problem; second-order ordinary differential equation; numerical experiments Citations:Zbl 0742.65067 PDFBibTeX XMLCite \textit{A. A. Abramov} and \textit{L. F. Yukno}, Differ. Equations 35, No. 2, 205--210 (1999; Zbl 0947.65093); translation from Differ. Uravn. 35, No. 2, 206--211 (1999)