Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 75, pp. 1-9.

Title: A second order ODE with a nonlinear final condition
   
Authors: Pablo Amster (Univ. de Buenos Aires, Argentina)
 Maria Cristina Mariani (Univ. de Buenos Aires, Argentina)
                 
Abstract:  
  We study a semilinear second-order ordinary differential
  equation with initial condition $u(0)=u_0$. We prove the 
  existence of solutions satisfying a nonlinear final condition 
  $u(T)=h'(u(T))$,  under a certain growth condition. 
  Also we state conditions ensuring that any solution with 
  Cauchy data $u(0) = u_0$, $u'(0)=v_0$ is defined  on the 
  whole interval $[0,T]$.
  
Submitted October 15, 2000. Published December 10, 2001.
Math Subject Classifications: 34B15, 34C37.
Key Words: Nonlinear boundary-value problems; fixed point methods.