From the introduction: We consider a model of dynamics of a population structured by size. This model consists in the differential equation \[ \frac{\partial x(t,l)}{\partial t}+\frac{\partial[g(l,e(t))x(t,l)]}{\partial l}=-[\mu(l,E(t))+u(l)]x(t,l), \] where \(x(t,l)\) is the density of individuals of size \(l\) at time \(t\), \(g\) and \(\mu\) are their growth and mortality coefficients, respectively, and the choice of a (measurable) control function \(u\) determines intensity of exploitation of the population. The function \(E\) characterizes intraspecific competition and has the form \[ E(t)=\int\limits^L_0\chi(l)x(t,l)dl, \] where \(\chi\) is a continuous nonnegative growing function, and the segment \([0,L]\), \(L>0\), is the range of sizes within which the population is cultivated.