Lyapunov-type inequalities for Laplacian systems and applications to boundary value problems
- College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Shijiazhuang, 050024, China.
- Department of Mathematics, The University of Hong Kong, Hong Kong, China.
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.
- Lyapunov type inequality
- boundary value problem
- Laplacian systems
T. Abdeljawad, A Lyapunov type inequality for fractional operators with nonsingular Mittag-Leffler kernel, J. Inequal. Appl., 2017 (2017), 11 pages.
R. P. Agarwal, A. Özbekler, Lyapunov type inequalities for second order forced mixed nonlinear impulsive differential equations, Appl. Math. Comput., 282 (2016), 216–225.
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.
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.
P. L. De Nápoli, J. P. Pinasco, Estimates for eigenvalues of quasilinear elliptic systems, J. Differential Equations, 227 (2006), 102–115.
S. Dhar, Q.-K. Kong, Lyapunov-type inequalities for higher order half-linear differential equations, Appl. Math. Comput., 273 (2016), 114–124.
M. Jleli, B. Samet, On Lyapunov-type inequalities for (p, q)-Laplacian systems, J. Inequal. Appl., 2017 (2017), 9 pages.
A. Tiryaki, D. Çakmak, M. F. Aktaş, Lyapunov-type inequalities for a certain class of nonlinear systems, Comput. Math. Appl., 64 (2012), 1804–1811.
X.-P.Wang, Lyapunov type inequalities for second-order half-linear differential equations, J. Math. Anal. Appl., 382 (2011), 792–801.
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.
X.-J. Yang, On inequalities of Lyapunov type, Appl. Math. Comput., 134 (2003), 293–300.