On discontinuous implicit evolution equations (Q1269675)

Let \(J\) be an interval of the form \([0,T]\) of the real line. The paper deals with an IVP of the form \[ f(t,u(t), Lu(t))= 0,\tag{\(*\)} \] for a.e. \(t\in J\), \(u(0)= u_0\). Here, \(u\) is a function on \(J\) to an ordered \(B\)-space \(E\), \(L\) is a differential-like operator with values in \(L^p(J,E)\) and \(f\) satisfies some monotonicity conditions. The authors provide existence results for extremal solutions which are monotone nonincreasing w.r.t. \(f\) and monotone nondecreasing w.r.t. \(u_0\). Several applications and examples close the paper.