The solutions on the right of Figure gif are merging (far offscreen) as , and they are ``straight'' enough to try using the theory of fences and funnels. In fact, as a result of Condition II, we see from equation (12) that as , solutions are going to behave very much like solutions to the equation . To be precise, from (12) we get

for all t > 0. Therefore, for any C, the curves

are respectively a lower fence and an upper fence for the differential equation (12). That is, for every t>0 the slope the slope of the direction field for at that point, and the slope of the direction field. Together these fences define an antifunnel , which is narrowing as ; see Figure gif. We will show in Appendix C that there is exactly one solution which is trapped in the narrowing antifunnel for all t>0, and that every solution of (12) for t > 0 is of this form for some C.
Annotation Form Interface

          Your name: 
     E-Mail address: 
 Annotation Subject: 
        Related URL: