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

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
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### References:

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