A class of evolution hemivariational inequalities. (English) Zbl 0920.47056

Liu, Zhenhai

Nonlinear Anal., Theory Methods Appl. 36, No. 1, A, 91-100 (1999).

The author studies the existence of solutions to the problem: Find \(u\in X= L^p(I,V)\) such that \(u(0)= 0\) and \[ \Biggl\langle{du\over dt}, v\Biggr\rangle_X+ \langle Au, v\rangle_X+ \int_I g^0(t, u,v)dt\geq \langle f,v\rangle_X,\quad\forall v\in X, \] where \(I= [0,T]\), \(V\subset X\subset V'\) forms an evolution triple, \(g^0(t,\cdot,\cdot)\) denotes the Clarke’s directional derivative and \(A\) is a map of class \((S_+)\) with respect to \(D(L)\) with \(Lu= {du\over dt}\).

Reviewer: V.Mustonen (Oulu)

MSC:

47J20	Variational and other types of inequalities involving nonlinear operators (general)
34G20	Nonlinear differential equations in abstract spaces

Keywords:

evolution hemivariational inequalities; Clarke’s directional derivative

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