Abstract
Green’s functions to 2-point simple type self-adjoint boundary value problems for bending of a beam under relatively strong tension on an elastic foundation are studied. We have 9 different Green’s functions. All are positive-valued and have a suitable hierarchical structure.
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References
N.V. Banichuk and A.U. Ishlinskii, Leonard Euler and mechanics of elastic systems (in Russian). Progress of Idea of Leonard Euler and Modern Science, NAUKA, 1988, 208–228.
Y.A. Melnikov, Influence Functions and Matrices. Marcel Dekker, 1999.
M. Toda, The Theory of Vibration (in Japanese). Baihukan, 1976.
S.P. Timoshenko and J.N. Goodier, Theory of Elasticity (in Japanese). Corona, 1976.
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Late Prof. M. Yamaguti gave to the first author profound influence on the directions of research and taught him the importance of application of mathematics to the other field of science. He continuously encouraged younger researchers. We all the authors express their hearty thanks to him.
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Kametaka, Y., Takemura, K., Suzuki, Y. et al. Positivity and hierarchical structure of Green’s functions of 2-point boundary value problems for bending of a beam. Japan J. Indust. Appl. Math. 18, 543–566 (2001). https://doi.org/10.1007/BF03168590
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DOI: https://doi.org/10.1007/BF03168590