- 00-140 P. Amster,M.-C. Mariani
- Nonlinear problems for a second order ODE
Mar 31, 00
(auto. generated ps),
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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 $[0,T]$.