Applications of the blowing-up construction and algebraic geometry to bifurcation problems

DOI10.1016/0022-0396(83)90102-XzbMath0464.34030MaRDI QIDQ1154033

Stephen Schecter, Michael A. Buchner, Jerrold E. Marsden

Publication date: 1983

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Hopf bifurcationnonlinear eigenvalue problemsvector-valued functionsMorse lemmahomogeneous equations of even degree

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Enumerative problems (combinatorial problems) in algebraic geometry (14N10)

Related Items

Hopf bifurcation at multiple eigenvalues with zero eigenvalue, Singularly perturbed systems, Existence of periodic solutions to nonlinear \(p\)-regular boundary value problem, An Iteration Method for Bifurcation Problem Involving Fredholm Mappings, New bifurcation theorems via the second-order optimality conditions, A note on \(C^ 1\) equivalence, Local bifurcation theory for multiparameter nonlinear eigenvalue problems, Periodic solutions of a forced Lotka-Volterra equation, Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shell, Bifurcation from degenerate solutions of equations involving lipschitz continuous mappings^∗, Global bifurcation of periodic solutions in nonlinear evolution problems with periodic forcing, Tangent vectors to a zero set at abnormal points., \(p\)-regular nonlinear dynamics, Numerical Liapunov-Schmidt spectral method for \(k\)-determined problems, An analytical study of bifurcation problems for equations involving Fredholm mappings, \(p\)-regular nonlinearity: tangency at singularity in degenerate optimization problems, Application of \(p\)-regularity theory to nonlinear boundary value problems, The Transformation of Vector-Functions, Scaling and Bifurcation, Bifurcation points of equations involving even multi-linear functions with application to elliptical differential equations, Degenerate Hopf bifurcation from multiple eigenvalues and stability, Bifurcation theorems via second-order optimality conditions, Bifurcation in the neighbourhood of a non-isolated singular point, Symmetry-breaking bifurcations on multidimensional fixed point subspaces, Symmetry and the bifurcation of capillary-gravity waves, On the zero set of G-equivariant maps, Multiparameter local bifurcation, Topological Triviality of a Family of Zero-Sets, Bifurcation at multiple eigenvalues and stability of bifurcating solutions, A generalization of the implicit function theorem for mappings from \({\mathcal R}^{n+1}\) into \({\mathcal R}^ n\) and its applications, Application of elliptic regularity to bifurcation in stationary nonlinear Schrödinger equations, Bifurcation problems for equations involving Lipschitz continuous mappings

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