Electron. J. Diff. Eqns., Vol. 2001(2001), No. 75, pp. 1-9.

A second order ODE with a nonlinear final condition

Pablo Amster & Maria Cristina Mariani

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.

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Pablo Amster
Departamento de Matematica,
Facultad de Ciencias Exactas y Naturales,
Universidad de Buenos Aires - CONICET,
Pab. I, Ciudad Universitaria,
(1428) Buenos Aires, Argentina
e-mail: pamster@dm.uba.ar
Maria Cristina Mariani
Departamento de Matematica,
Facultad de Ciencias Exactas y Naturales,
Universidad de Buenos Aires - CONICET,
Pab. I, Ciudad Universitaria,
(1428) Buenos Aires, Argentina
e-mail: mcmarian@dm.uba.ar

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