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An existence theorem for systems of boundary value problems
Authors:Gerd Herzog  Roland Lemmert
Institution:Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany ; Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Abstract:We prove an existence theorem for $u'(t)=f(t,u(t),u'(t))$, $u(0)=u_0$, $u(1)=u_1$ in $\mathbb{R}^n$, using the shooting method. The function $f$ is supposed to be asymptotically linear.

Keywords:Dirichlet problem  shooting function  existence theorem
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