A Topological Fixed-Point Index Theory for Evolution Inclusions
نویسنده
چکیده
In the paper we construct a topological fixed-point theory for a class of set-valued maps which appears in natural way in boundary value problems for differential inclusions. Our construction is based upon the notion of (U, V )-approximation in the sense of Ben-El-Mechaiekh and Deguire. As applications we consider initial-value problems for nonlinear evolution inclusions of the type x′(t) ∈ −A(t, x(t)) + F (t, x(t)) x(0) = x0 ) where the operator A satisfies various monotonicity assumptions and F is an upper semicontinuous set-valued perturbation.
منابع مشابه
Special Session 67: Topological Methods for the Qualitative Analysis of Differential Equations and Inclusions
The main topic of the session will be topological methods such as degree theory, fixed point index theory, Morse theory, Maslov index, spectral flow, and their applications to various problems in ordinary, functional and partial differential equations, differential-algebraic equations and differential inclusions. Particular emphasis will be given to existence, multiplicity and bifurcation of so...
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