Global bifurcation theory via Galerkin's method

DOI10.1016/0362-546X(77)90038-4zbMath0477.47036OpenAlexW1989651512MaRDI QIDQ3935022

John F. Toland

Publication date: 1977

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

Full work available at URL: https://doi.org/10.1016/0362-546x(77)90038-4

zbMATH Keywords

global bifurcationA-proper mappingsmultivalued degree

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Nonlinear elliptic equations (35J60) Degree, winding number (55M25)

Related Items (16)

Topological degree and A-proper operators ⋮ A vector parameter global bifurcation result ⋮ Fredholm theory for abstract and differential equations with noncompact nonlinear perturbations of Fredholm maps ⋮ Unnamed Item ⋮ Bifurcation of A-proper mappings without transversality considerations ⋮ Global results concerning bifurcation for Fredholm maps of index zero with a transversality condition ⋮ A generalization of Leray-Schauder theorem and surjectivity results for multivalued A-proper and pseudo A-proper mappings ⋮ A generalized-degree homotopy yielding global bifurcation results ⋮ Global bifurcation of a class of periodic boundary-value problems ⋮ Some generalizations of the first Fredholm theorem to multivalued A- proper mappings with applications to nonlinear elliptic equations ⋮ Using degree theory for densely defined A-proper maps in the solvability of semilinear equations with unbounded and noninvertible linear part ⋮ Qualitative methods in bifurcation theory ⋮ Galerkin approximations in several parameter bifurcation problems ⋮ \(A\)-properness and fixed point theorems for sums of dissipative and ball-condensing maps ⋮ Existence theorems for sums of K-ball contractions and accretive operators via A-proper mappings ⋮ Periodic solutions of nonlinear second-order differential equations which are not solvable for the highest derivative

Cites Work

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• Existence theory for the Hartree equation
• Global solution branches for positive mappings
• Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces
• Some global results for nonlinear eigenvalue problems
• The fixed point index for local condensing maps
• Large nonlinearities and monotonicity
• Some Bifurcation Theory for k -Set Contractions
• On the approximation-solvability of equations involving 𝐴-proper and pseudo-𝐴-proper mappings
• Non-compact positive operators
• LIMIT-COMPACT AND CONDENSING OPERATORS
• The Fixed Point Index of a Linear K -Set Contraction
• On Seminorms of Operators

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