A Second Order ODE with a Nonlinear Final Condition
Mariani, Maria Cristina
Southwest Texas State University, Department of Mathematics
We study a semilinear second-order ordinary differential equation with initial condition u(0) = u0. 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) = u0, u'(0) = v0 is defined on the whole interval [0, T].
Nonlinear boundary-value problems, Fixed point methods
Amster, P., & Mariani, M. C. (2001). A second order ODE with a nonlinear final condition. <i>Electronic Journal of Differential Equations, 2001</i>(75), pp. 1-9.