Symmetric Hopf bifurcation in implicit neutral functional differential equations: Equivariant degree approach

Balanov, Zalman; Krawcewicz, Wiesław; Li, Zhichao

doi:10.1007/s11784-015-0209-4

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“…The degree theory was applied in [7] to obtain nontrivial solutions to multivalued boundary value problems. See also [9,10] for further applications of that degree to obtain multiple solutions to some implicit functional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree

Dzedzej

Gzella

2020

Mathematics

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Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f. This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient mappings.

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Section: Introductionmentioning

confidence: 99%