P. Amster,M.-C. Mariani
Nonlinear problems for a second order ODE
(30K, TeX)

ABSTRACT.  We study the general class of semilinear second order 
ordinary differential equations $u''(t)+r(t) u'(t) + g(t,u(t)) = f(t)$ 
with a fixed constraint $u(0) = u_0$. 
Under a growth condition on $g$ 
we prove the existence of solutions satisfying the 
nonlinear condition $u(T)=h(u'(T))$. 
Moreover, we give conditions in order to 
assure that any solution satisfying a 
Cauchy condition $u(0) = u_0, \quad u'(0)=v_0$ is defined over $[0,T]$.