On the existence of singular solutions.
In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive...
In the paper, we give an existence theorem of periodic solution for Liénard equation , . As a result, we estimate the amplitude (maximal -value) of the limit cycle of the van der Pol equation , from above by for every . The result is an improvement of the author’s previous estimation .