On calculation of the bifurcations by the fibering approach. (English) Zbl 1132.35306
Chuong, N.M. (ed.) et al., Harmonic, wavelet and \(p\)-adic analysis. Based on the summer school, Quy Nhon, Vietnam, June 10–15, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-549-5/hbk). 141-155 (2007).
Summary: In this contribution we discuss problems of the nonlocal analysis of bifurcations for equations of variational form. This includes the calculation of the bifurcation values \(\lambda_i\), the construction of the branches of solutions on \((\lambda_i, \lambda_{i+1})\), and the study of their asymptotic behaviour at the bifurcation \(\lambda\to\lambda_i\). We present a survey of results where these problems are solved using the method based on fiber spectral analysis.
For the entire collection see [Zbl 1117.42001].
For the entire collection see [Zbl 1117.42001].
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35J20 | Variational methods for second-order elliptic equations |
| 47J15 | Abstract bifurcation theory involving nonlinear operators |
| 35A15 | Variational methods applied to PDEs |
| 58E07 | Variational problems in abstract bifurcation theory in infinite-dimensional spaces |
