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 Mat. Sb., 2016, Volume 207, Number 12, Pages 3–29 (Mi msb8369)

Global bifurcation of solutions of certain nonlinear eigenvalue problems for ordinary differential equations of fourth order

Z. S. Aliyevab

a Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
b Faculty of Mechanics and Mathematics, Baku State University, Azerbaijan

Abstract: Nonlinear eigenvalue problems are investigated for ordinary differential equations of fourth order. Local and global bifurcations of nontrivial solutions of these problems are investigated. It is shown that the set of nontrivial solutions of the problems under consideration that bifurcate from points and intervals of the line of trivial solutions contains unbounded continua.
Bibliography: 42 titles.

Keywords: bifurcation point, bifurcation interval, eigenvalue, eigenfunction, continuum of solutions.

DOI: https://doi.org/10.4213/sm8369

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English version:
Sbornik: Mathematics, 2016, 207:12, 1625–1649

Bibliographic databases:

UDC: 517.927.25
MSC: Primary 34B15, 34C23; Secondary 34B08

Citation: Z. S. Aliyev, “Global bifurcation of solutions of certain nonlinear eigenvalue problems for ordinary differential equations of fourth order”, Mat. Sb., 207:12 (2016), 3–29; Sb. Math., 207:12 (2016), 1625–1649

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8369
• https://doi.org/10.4213/sm8369
• http://mi.mathnet.ru/eng/msb/v207/i12/p3

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. R. A. Huseynova, “Global bifurcation from principal eigenvalues for nonlinear fourth order eigenvalue problem with indefinite weight”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 42:2 (2016), 202–211
2. Z. S. Aliyev, R. A. Huseynova, “Bifurcation in nonlinearizable eigenvalue problems for ordinary differential equations of fourth order with indefinite weight”, Electron. J. Qual. Theory Differ. Equ., 2017, 92, 12 pp.
3. N. A. Mustafayeva, “On the structure of global continua of solutions bifurcating from infinity of some nonlinear fourth order eigenvalue problems”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 43:2 (2017), 270–277
4. Z. S. Aliyev, N. A. Mustafayeva, “Bifurcation of solutions from infinity for certain nonlinear eigenvalue problems of fourth-order ordinary differential equations”, Electron. J. Differ. Equ., 2018, 98, 19 pp.
5. Z. S. Aliyev, R. A. Huseynova, “Global bifurcation from infinity in some nonlinearizable eigenvalue problems with indefinite weight”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 44:1 (2018), 123–134
6. P. R. Manafova, “Bifurcation of solutions of nonlinearizable Dirac problems with spectral parameter in the boundary condition”, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 44:2 (2018), 318–327
7. Z. S. Aliyev, Sh. M. Hasanova, “Global bifurcation of positive solutions of semi-linear elliptic partial differential equations with indefinite weight”, Z. Anal. Anwend., 38:1 (2019), 1–15
8. Rzayeva H.Sh., “Global Bifurcation From Infinity in Nonlinear One Dimensional Dirac Problems”, Proc. Inst. Math. Mech., 45:1 (2019), 146–154
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