The global structure of the zero set of a family of semilinear Fredholm maps

DOI10.1016/0362-546X(91)90074-BzbMath0812.47060OpenAlexW1994227383MaRDI QIDQ3980056

Thomas J. Bartsch

Publication date: 26 June 1992

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(91)90074-b

zbMATH Keywords

Dirac operatorsvector bundlecontinuation theoremglobal implicit function theoremSturm-Liouville boundary value problemscompact perturbationcodegreebifurcation theorembifurcation of zeroeslinear Fredholm operator of index 0obstruction to the existence of a global parametrixzero set of a family of semilinear Fredholm maps

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Fixed-point theorems (47H10) Degree theory for nonlinear operators (47H11) Fixed-point theorems on manifolds (58C30) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) (Semi-) Fredholm operators; index theories (47A53) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (7)

Bifurcations of a parametrized family of boundary value problems for second order differential inclusions ⋮ A remark on bifurcation of Fredholm maps ⋮ Non‐Zero Space Charge Approximation of Thyristors ⋮ The index bundle for selfadjoint Fredholm operators and multiparameter bifurcation for Hamiltonian systems ⋮ Fredholm theory of families of discrete dynamical systems and its applications to bifurcation theory ⋮ Global bifurcation of homoclinic trajectories of discrete dynamical systems ⋮ The index bundle and multiparameter bifurcation for discrete dynamical systems

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