BIFURCATION OF SOLUTIONS TO A NONLINEAR ELLIPTIC PROBLEM IN A DISK
DOI:
https://doi.org/10.5281/zenodo.20487048Keywords:
nonlinear elliptic equation, bifurcation, Lyapunov–Schmidt method, asymptotic expansion, Rabinowitz theorem, moving-planes method.Abstract
We study a nonlinear elliptic Dirichlet boundary value problem for an equation in a circular domain. Using the method of small parameters and the Lyapunov–Schmidt reduction, we investigate bifurcation points, construct asymptotic expansions of solutions, and determine the nature of the emerging branches. The existence of a supercritical pitchfork bifurcation is proved. The stability of solutions and the global structure of branches are analysed.
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References
1. Krasnosel'skij M.A. Bifurcation of Solutions of Nonlinear Equations. Moscow: Nauka.
2. Rabinowitz P. Global bifurcation theory. Uspekhi Mat. Nauk.
3. Vladimirov V.S. Equations of Mathematical Physics. Moscow: Nauka.
4. Smirnov V.I. A Course of Higher Mathematics. Vol. IV. Moscow: Nauka.
5. Gilbarg D., Trudinger N. Elliptic Partial Differential Equations of Second Order. Berlin: Springer.
6. Chow S., Hale J. Methods of Bifurcation Theory. New York: Springer.
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