Abstract
We suggest the construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type. We describe the main properties of this characteristic, including applications to coincidence points. An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given.
Highlights
The necessity of studying coincidence points of Fredholm operators and nonlinear maps of various classes arises in the investigation of many problems in the theory of partial differential equations and optimal control theory
For inclusions with linear Fredholm operators, a number of such topological invariants was studied in the works [7, 8, 13, 18, 19]
We suggest the general construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type
Summary
The necessity of studying coincidence points of Fredholm operators and nonlinear (compact and condensing) maps of various classes arises in the investigation of many problems in the theory of partial differential equations and optimal control theory (see, e.g., [3, 4, 7, 13, 17, 18, 20,21,22]). We suggest the general construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type.
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