P.Amster, M.C. Mariani
Nonlinear two-point boundary value problems and a Duffing equation
(23K, TEX)

ABSTRACT.  In this paper we study a general semilinear 
second order ODE 
$$(pu')'+g(t,u,u') = f \tag{*}$$ 
Under an appropiate 
growth condition 
on $g$ we prove that 
the 
Dirichlet problem for (*) is uniquely 
solvable. 
Moreover, the set of $H^2$-solutions 
of (*) is homeomorphic 
to the two-dimensional real space. 
We also establish conditions for 
the existence of 
periodic solutions of (*).