Lyapunov-type inequalities for Laplacian systems and applications to boundary value problems

Volume 11, Issue 1, pp 8--16 http://dx.doi.org/10.22436/jnsa.011.01.02

Publication Date: December 22, 2017 Submission Date: September 15, 2017 Revision Date: November 09, 2017 Accteptance Date: November 16, 2017

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Authors

Qiao-Luan Li - College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Shijiazhuang, 050024, China. Wing-Sum Cheung - Department of Mathematics, The University of Hong Kong, Hong Kong, China.

Abstract

In this paper, we establish some new Lyapunov-type inequalities for a class of Laplacian systems. With these, sufficient conditions for the non-existence of nontrivial solutions to certain boundary value problems are obtained. A lower bound for the eigenvalues is also deduced.

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Keywords

• Lyapunov type inequality
• boundary value problem
• Laplacian systems

MSC

•  26D15
•  26D10
•  34B15

References

• [1] T. Abdeljawad, A Lyapunov type inequality for fractional operators with nonsingular Mittag-Leffler kernel, J. Inequal. Appl., 2017 (2017), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] R. P. Agarwal, A. Özbekler, Lyapunov type inequalities for second order forced mixed nonlinear impulsive differential equations, Appl. Math. Comput., 282 (2016), 216–225.
  • View Article
  • MathSciNet
  • Google Scholar


• [3] M. F. Aktaş, D. Çakmak, A Tiryaki, On the Lyapunov-type inequalities of a three-point boundary value problem for third order linear differential equations, Appl. Math. Lett., 45 (2015), 1–6.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] L.-Y. Chen, C.-J. Zhao, W.-S. Cheung, On Lyapunov-type inequalities for two-dimensional nonlinear partial systems, J. Inequal. Appl., 2010 (2010), 12 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] P. L. De Nápoli, J. P. Pinasco, Estimates for eigenvalues of quasilinear elliptic systems, J. Differential Equations, 227 (2006), 102–115.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] S. Dhar, Q.-K. Kong, Lyapunov-type inequalities for higher order half-linear differential equations, Appl. Math. Comput., 273 (2016), 114–124.
  • View Article
  • MathSciNet
  • Google Scholar


• [7] M. Jleli, B. Samet, On Lyapunov-type inequalities for (p, q)-Laplacian systems, J. Inequal. Appl., 2017 (2017), 9 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] A. Tiryaki, D. Çakmak, M. F. Aktaş, Lyapunov-type inequalities for a certain class of nonlinear systems, Comput. Math. Appl., 64 (2012), 1804–1811.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] X.-P.Wang, Lyapunov type inequalities for second-order half-linear differential equations, J. Math. Anal. Appl., 382 (2011), 792–801.
  • View Article
  • MathSciNet
  • Google Scholar


• [10] Y.-Y. Wang, Y.-N. Li, Y.-Z. Bai, Lyapunov-type inequalities for quasilinear systems with antiperiodic boundary conditions, Russian version appears in Ukraïn. Mat. Zh., 65 (2013), 1646–1656, Ukrainian Math. J., 65 (2014), 1822–1833.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] X.-J. Yang, On inequalities of Lyapunov type, Appl. Math. Comput., 134 (2003), 293–300.
  • View Article
  • MathSciNet
  • Google Scholar