Optimal stationary solution in forest management model by accounting intra-species competition

We consider a model of exploitation of a size-structured population when the birth, growth and mortality rates depend on the individual size and interspecies competition, while the exploitation intensity is a function of the size only. For a given exploitation intensity and under natural assumptions on the rates, we establish existence and uniqueness of a nontrivial stationary state of the population. In addition, we prove existence of an exploitation intensity which maximises a selected profit functional of exploitation.