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Second Variation Condition and Quadratic Integral Inequalities with Higher Order Derivatives

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Abstract

The positivity of quadratic integrals involving variable coefficients and derivatives of any order is studied. The result is determined by the solution of an initial value problem for a system of first order nonlinear differential equations. The system is identified as the matrix Riccati differential equation in control theory. A complete conclusion is reached by considering the cases when the solution is bounded and when the solution is unbounded.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Houston, Houston, TX, 77204, U.S.A.

    Yi-Chao Chen

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  1. Yi-Chao Chen
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Chen, YC. Second Variation Condition and Quadratic Integral Inequalities with Higher Order Derivatives. Journal of Elasticity 70, 111–127 (2003). https://doi.org/10.1023/B:ELAS.0000005583.55075.77

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  • DOI: https://doi.org/10.1023/B:ELAS.0000005583.55075.77

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