Slowly Oscillating Solutions for Differential Equations with Strictly Monotone Operator

The authors discuss necessary and sufficient conditions for the existence and uniqueness of slowly oscillating solutions for the differential equation u'+F(u)=h(t) with strictly monotone operator. Particularly, the authors give necessary and sufficient conditions for the existence and uniqueness of slowly oscillating solutions for the differential equation u'+ ￠ |(u)=h(t), where ￠ | denotes the gradient of the convex function | on ￠ N.