Bifurcation points of equations involving even multi-linear functions with application to elliptical differential equations. (English) Zbl 0721.47046
The author studies problems on bifurcation from zero on Banach spaces. By using what are by now rather classical techniques of rescaling and degree theory, he obtains conditions implying local bifurcation.
Reviewer: E.Dancer (Armidale)
MSC:
| 47J05 | Equations involving nonlinear operators (general) |
| 47H11 | Degree theory for nonlinear operators |
| 58E07 | Variational problems in abstract bifurcation theory in infinite-dimensional spaces |
| 35J40 | Boundary value problems for higher-order elliptic equations |
References:
| [1] | DOI: 10.1016/0022-0396(83)90102-X · Zbl 0464.34030 · doi:10.1016/0022-0396(83)90102-X |
| [2] | Deimling K., Nonlinear Functional Analysis (1985) · Zbl 0559.47040 |
| [3] | Gilbarg, D. and Trudinger, N. S. 1977. ”Elliptic partial differential equations of second order”. Berlin Heidelberg New York: Springer – Verlag. · Zbl 0361.35003 |
| [4] | Greub W. H., Linear Algebra (1967) |
| [5] | DOI: 10.1016/0022-1236(73)90030-X · Zbl 0275.47045 · doi:10.1016/0022-1236(73)90030-X |
| [6] | Rafel, G. G. 1982. ”Asymptotic solutions for a class of nonlinear vibration problems”. University of Utrecht Holland. Ph.D.Thesis |
| [7] | Tan N. X., Bifurcation problems for equations involving Lipschitz continuous mappings (1982) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
