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An existence theorem for systems
of boundary value problems


Authors: Gerd Herzog and Roland Lemmert
Journal: Proc. Amer. Math. Soc. 128 (2000), 157-160
MSC (1991): Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-99-05011-X
Published electronically: June 21, 1999
MathSciNet review: 1622754
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. Deimling, K.: Ordinary differential equations in Banach spaces. Lecture Notes in Mathematics, 596, Springer, 1977. MR 57:3546
  • 2. Deimling, K.: Nonlinear functional analysis. Springer, 1985. MR 86j:47001
  • 3. Hartman, P.: Ordinary Differential equations. John Wiley & Sons, 1964. MR 30:1270
  • 4. 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).
  • 5. Lemmert, R.: The shooting method for some nonlinear Sturm-Liouville boundary value problems. J. Appl. Math. Phys. 40 (1989), 769-773. MR 90m:65153
  • 6. 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: https://doi.org/10.1090/S0002-9939-99-05011-X
Keywords: Dirichlet problem, shooting function, existence theorem
Received by editor(s): March 10, 1998
Published electronically: June 21, 1999
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society

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