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An existence theorem for systems of boundary value problems

Author(s): Gerd Herzog; Roland Lemmert
Journal: Proc. Amer. Math. Soc. 128 (2000), 157-160.
MSC (1991): Primary 34B15
Posted: June 21, 1999
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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.

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Deimling, K.: Nonlinear functional analysis. Springer, 1985. MR 86j:47001
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Hartman, P.: Ordinary Differential equations. John Wiley & Sons, 1964. MR 30:1270
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Herzog, G., Lemmert, R.: On the structure of the solution set of $u''=f(t,u)$, $u(0)=u(1)=0$. Math. Nachr. (to appear).
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Lemmert, R.: The shooting method for some nonlinear Sturm-Liouville boundary value problems. J. Appl. Math. Phys. 40 (1989), 769-773. MR 90m:65153
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Krasnoselskii, M.A., Perow, A.I., Powolozki, A.I., Sabrejko, P.P.: Vektorfelder in der Ebene. Akademie-Verlag Berlin, 1966. MR 34:1995

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Additional Information:

Gerd Herzog
Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: Gerd.Herzog@math.uni-karlsruhe.de

Roland Lemmert
Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Email: Roland.Lemmert@math.uni-karlsruhe.de

DOI: 10.1090/S0002-9939-99-05011-X
PII: S 0002-9939(99)05011-X
Keywords: Dirichlet problem, shooting function, existence theorem
Received by editor(s): March 10, 1998
Posted: June 21, 1999
Communicated by: Hal L. Smith
Copyright of article: Copyright 1999, American Mathematical Society

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