Geodesic
A second order ODE with a nonlinear final condition
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $[0,T]$.
Classification : 34B15, 34C37
Keywords: nonlinear boundary-value problems, fixed point methods 
@article{EJDE_2001__2001__a34,
     author = {Amster, Pablo and Mariani, Mar{\'\i}a Cristina},
     title = {A second order {ODE} with a nonlinear final condition},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a34/}
}
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Amster, Pablo; Mariani, María Cristina. A second order ODE with a nonlinear final condition. Electronic Journal of Differential Equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a34/