## Convex and nonconvex perturbations of evolution equations. (Perturbations convexes et non convexes des équations d’évolution.)(French)Zbl 0863.47050

Summary: This paper is concerned with the evolution inclusion $$x'\in-Ax+F(t,x)$$, where $$A$$ is an $$m$$-accretive operator and $$F$$ is a weakly compact valued multifunction measurable in $$t$$, upper semicontinuous in $$x$$. We prove the existence of solutions under various assumptions on the operator $$A$$ and the perturbation $$F$$.

### MSC:

 47H20 Semigroups of nonlinear operators 47H06 Nonlinear accretive operators, dissipative operators, etc. 34A60 Ordinary differential inclusions 54C65 Selections in general topology
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