A nonlinear inequality and evolution problems

A. G. Ramm

Assume that $g(t)\ge 0$, and $$\dot{g}(t)\le -\gamma (t)g(t)+\alpha (t,g(t))+\beta (t),t\ge 0;g(0)=g_0;\dot{g}:=\frac{dg}{dt},$$ on any interval $[0,T)$ on which $g$ exists and ha…