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Riemann zeta function and Lyapunov-type inequalities for certain higher order differential equations |
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| Authors: | Kohtaro Watanabe Hiroyuki Yamagishi |
| Institution: | a Department of Computer Science, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan b Tokyo Metropolitan College of Industrial Technology, 1-10-40 Higashi-ooi, Shinagawa, Tokyo 140-0011, Japan c Faculty of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka 560-8531, Japan |
| Abstract: | This note generalizes the well known Lyapunov-type inequalities for second-order linear differential equations to certain 2M-th order linear differential equations with five types of boundary conditions. The usage of the best constant of some Sobolev-type inequalities clarify the process for obtaining such inequality and sharpen the result of Çakmak 2]. |
| Keywords: | Lyapunov inequality Sobolev inequality Best constant Riemann zeta function |
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