Global Bifurcation from Zero in Some Fourth-Order Nonlinear Eigenvalue Problems
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 o...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2021-03, Vol.44 (2), p.981-992 |
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| container_title | Bulletin of the Malaysian Mathematical Sciences Society |
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| creator | Aliyev, Z. S. Asadov, X. A. |
| description | 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. |
| doi_str_mv | 10.1007/s40840-020-00989-6 |
| format | Article |
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S.</creatorcontrib><creatorcontrib>Asadov, X. A.</creatorcontrib><title>Global Bifurcation from Zero in Some Fourth-Order Nonlinear Eigenvalue Problems</title><title>Bulletin of the Malaysian Mathematical Sciences Society</title><addtitle>Bull. Malays. Math. Sci. Soc</addtitle><description>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. 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| subjects | Applications of Mathematics Bifurcations Boundary conditions Differential equations Eigenvalues Eigenvectors Mathematics Mathematics and Statistics Ordinary differential equations |
| title | Global Bifurcation from Zero in Some Fourth-Order Nonlinear Eigenvalue Problems |
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