On coincidence index for multivalued perturbations of nonlinear Fredholm maps and some applications.

Obukhovskii, Valeri; Zecca, Pietro; Zvyagin, Victor

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Displaying similar documents to “On coincidence index for multivalued perturbations of nonlinear Fredholm maps and some applications.”

The coincidence index for fundamentally contractible multivalued maps with nonconvex values

Dorota Gabor (2000)

Annales Polonici Mathematici

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We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given. ...

An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations.

Obukhovskii, Valeri, Zecca, Pietro, Zvyagin, Victor (2006)

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Andrzej Granas (1972)

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A degree theory for a class of perturbed Fredholm maps. II.

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Systems of Inclusions Involving Fredholm Operators and Noncompact Maps

Dorota Gabor (2007)

Bollettino dell'Unione Matematica Italiana

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We consider the existence of solutions to the system of two inclusions involving Fredholm operators of nonnegative index and the so-called fundamentally restrictible maps with not necessarily convex values. We apply the technique of a solution map and, since the assumptions admit a 'dimension defect', we use the coincidence index, i.e. the homotopy invariant based on the cohomotopy theory. Two examples of applications to boundary value problems are included.