A Second Order ODE with a Nonlinear Final Condition
MetadataShow full metadata
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].