A Bifurcation Theorem for Potential Operators with Infinite Dimensional Kernel
Copyright policy )A Bifurcation Theorem for Potential Operators with Infinite Dimensional Kernel
Let \(X\) be a Hilbert space and \(f: X\to \mathbb{R}\) a smooth function with \(f'(0)= 0\). The authors study the equation \(f'(x)= \lambda x\) under the assumption that \(f'\) satisfies a Palais-Smale condition. They show, in particular, that every isolated eigenvalue of \(f''(0)\) is a bifurcation point.
- Arizona State University United States
Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Equations involving nonlinear operators (general), Applied Mathematics, Palais-Smale condition, smooth function, bifurcation point, Analysis
Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Equations involving nonlinear operators (general), Applied Mathematics, Palais-Smale condition, smooth function, bifurcation point, Analysis
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!