Geodesic
A second order ODE with a nonlinear final condition
Electronic journal of differential equations, Tome 2001 (2001)
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},
     year = {2001},
     volume = {2001},
     zbl = {0997.34015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a34/}
}
TY  - JOUR
AU  - Amster,  Pablo
AU  - Mariani,  María Cristina
TI  - A second order ODE with a nonlinear final condition
JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
UR  - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a34/
LA  - en
ID  - EJDE_2001__2001__a34
ER  - 
%0 Journal Article
%A Amster,  Pablo
%A Mariani,  María Cristina
%T A second order ODE with a nonlinear final condition
%J Electronic journal of differential equations
%D 2001
%V 2001
%U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a34/
%G en
%F EJDE_2001__2001__a34
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/