00-140 P. Amster,M.-C. Mariani

Nonlinear problems for a second order ODE (30K, TeX) Mar 31, 00

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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 $[0,T]$.

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