A Second Order ODE with a Nonlinear Final Condition
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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].
CitationAmster, P., & Mariani, M. C. (2001). A second order ODE with a nonlinear final condition. Electronic Journal of Differential Equations, 2001(75), pp. 1-9.
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