Summary: Let H be a real Hilbert space with inner product (.,.), U a nonempty and open subset in H, \(A: D(A)\subset H\to 2^ H\) an m-accretive operator and B: [0,T]\(\times U\to H\) a given function. Let us consider the strongly nonlinear perturbed evolution equation \[ (1)\quad \frac{du}{dt}(t)+Au(t)\ni B(t,u(t)),\quad 0\leq t\leq T,\quad u(0)=u_ 0, \] where \(u_ 0\in U\cap \overline{D(A)}\). The aim of this note is to state a local existence result concerning integral solutions for (1) which generalizes a previous theorem due to E. Schechter [Isr. J. Math. 43, 49-61 (1982; Zbl 0516.34060)].