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Global Bifurcation from Zero in Some Fourth-Order Nonlinear Eigenvalue Problems

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Abstract

In this paper, we study the nonlinear eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in the boundary condition. Global bifurcation of nontrivial solutions of this problem is investigated. We prove the existence of two families of unbounded continua of the set of solutions to this problem bifurcating from points and intervals of the line of trivial solutions. Moreover, it is shown that these continua are contained in classes of functions possessing oscillating properties of the eigenfunctions of the corresponding linear problem and their derivatives.

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Acknowledgements

The authors are deeply grateful to the referees for their valuable comments and suggestions, which made a significant contribution to the improvement in the text of the article and an understanding of the results.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Baku State University, 1148, Baku, Azerbaijan

    Z. S. Aliyev

  2. Department of Differential Equations, Institute of Mathematics and Mechanics NAS of Azerbaijan, 1141, Baku, Azerbaijan

    Z. S. Aliyev

  3. Baku Ataturk Lyceum, 1010, Baku, Azerbaijan

    X. A. Asadov

Authors
  1. Z. S. Aliyev
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  2. X. A. Asadov
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Correspondence to Z. S. Aliyev.

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Communicated by Shangjiang Guo.

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Aliyev, Z.S., Asadov, X.A. Global Bifurcation from Zero in Some Fourth-Order Nonlinear Eigenvalue Problems. Bull. Malays. Math. Sci. Soc. 44, 981–992 (2021). https://doi.org/10.1007/s40840-020-00989-6

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  • DOI: https://doi.org/10.1007/s40840-020-00989-6

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