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On a class of evolution equations without convexity. (English) Zbl 0880.47045

The authors study perturbations of the differential inclusion \(u'\in-Au\), \(u(0)=u_0\), where \(A\) is the subdifferential of a nonconvex function of \(\varphi\)-monotone of order 2 class. It is proved a weak-strong continuous dependence of the solution on a single-valued perturbation depending only on time and an existence result in the case of additive nonconvex valued perturbation.

MSC:

47H20 Semigroups of nonlinear operators
47H05 Monotone operators and generalizations
49J52 Nonsmooth analysis
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