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On Systems of Boundary Value Problems for Differential Inclusions

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Abstract

Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein–Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.

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Authors and Affiliations

  1. Department of Mathematics, The University of Nebraska–Lincoln, Lincoln, NE 68588–0130, USA

    Lynn Erbe

  2. School of Mathematics and Statistics, The University of New South Wales, Sydney, 2052, Australia

    Christopher C. Tisdell

  3. School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Patricia J. Y. Wong

Authors
  1. Lynn Erbe
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  2. Christopher C. Tisdell
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  3. Patricia J. Y. Wong
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Corresponding author

Correspondence to Christopher C. Tisdell.

Additional information

This research is supported by the Australian Research Council’s Discovery Projects (DP0450752) and Linkage International (LX0561259)

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Erbe, L., Tisdell, C.C. & Wong, P.J.Y. On Systems of Boundary Value Problems for Differential Inclusions. Acta Math Sinica 23, 549–556 (2007). https://doi.org/10.1007/s10114-005-0901-1

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  • DOI: https://doi.org/10.1007/s10114-005-0901-1

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