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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 \(q(t,\lambda)\).

MSC:

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators

Citations:

Zbl 0742.65067
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