The aftermath of the intermediate value theorem.
The coincidence index for fundamentally contractible multivalued maps with nonconvex values
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.
The degree of proper C2 Fredholm mapppings I.
The generalized Conley index and multiple solutions of semilinear elliptic problems.
The nonlinear periodic second order boundary value problem
The periodic problem for semilinear differential inclusions in Banach spaces
Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.
The product formula.
A useful property of the Brouwerdegree relates the degree of a composition of maps to the degree of each map. This property, which can be generalized for the Leray Schauder degree and in some cases for the A-proper maps is called the Product Formula. In a previous paper we developed a generalized degree theory for a class of mappings, this class contains the class of A-proper mappings and compact mappings. In this paper we prove a generalization of the Product Formula when one factor is of the Identity+Compact...
The semilinear Feng and FMV spectra.
The topological degree method for equations of the Navier-Stokes type.
Topological and approximation methods of degree theory of set-valued maps [Book]
Topological degree and application to a parabolic variational inequality problem.
Topological degree for maximal monotone operators and application to parametric optimization problems.
Two topological definitions of a Nielsen number for coincidences of noncompact maps.