Geodesic
Computation of the minimal eigenvalue for a nonlinear Sturm–Liouville problem
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 91-104

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We derive a condition for the existence of the minimal eigenvalue answering the positive eigenfunction of the nonlinear eigenvalue problem for an ordinary differential equation. This problem is approximated by a mesh scheme of the finite element method. The convergence of the approximate solutions to the exact ones is investigated. The theoretical results are illustrated by numerical experiments for a model problem.
Keywords: eigenvalue, positive eigenfunction, nonlinear eigenvalue problem, ordinary differential equation, finite element method.
Mots-clés : Sturm–Liouville problem 
@article{UZKU_2013_155_3_a9,
     author = {V. S. Zheltukhin and S. I. Solov'ev and P. S. Solov'ev and V. Yu. Chebakova},
     title = {Computation of the minimal eigenvalue for a~nonlinear {Sturm{\textendash}Liouville} problem},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {91--104},
     publisher = {mathdoc},
     volume = {155},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_3_a9/}
}
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V. S. Zheltukhin; S. I. Solov'ev; P. S. Solov'ev; V. Yu. Chebakova. Computation of the minimal eigenvalue for a nonlinear Sturm–Liouville problem. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 3, pp. 91-104. http://geodesic.mathdoc.fr/item/UZKU_2013_155_3_a9/