Periodic boudary-value problem for Hill's equation in the case of parametric resonance

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Necessary and sufficient conditions for the existence of solutions of nonlinear nonautonomous periodic problem for Hill’s equation in the case of parametric resonance. A characteristic feature of the task is the need of finding, as desired solution, and the corresponding eigenfunction, which ensures solvability of the periodic problem for Hill’s equation in the case of parametric resonance. To construct solutions of the periodic problem for Hill’s equation and the corresponding eigenfunction in the case of parametric resonance proposed iterative scheme, based on the method of simple iterations with used list-square technics.

Keywords: nonlinear nonautonomous periodic boudary-value problem, Hill’s equation, the case of parametric resonance, he method of simple iterations
Citation in English: Chujko S.M., Starkova O.V., Kulish P.V. Periodic boudary-value problem for Hill's equation in the case of parametric resonance // Computer Research and Modeling, 2014, vol. 6, no. 1, pp. 27-43
Citation in English: Chujko S.M., Starkova O.V., Kulish P.V. Periodic boudary-value problem for Hill's equation in the case of parametric resonance // Computer Research and Modeling, 2014, vol. 6, no. 1, pp. 27-43
DOI: 10.20537/2076-7633-2014-6-1-27-43
According to Crossref, this article is cited by:
  • Sergey Mikhaylovich Chujko, O. V. Nesmelova (Starkova), D. V. Sysoev. Nonlinear boudary value problem in the case of parametric resonance. // Computer Research and Modeling. 2015. — V. 7, no. 4. — P. 821. DOI: 10.20537/2076-7633-2015-7-4-821-833
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