Lyapunov-Type Inequalities for Some Quasilinear Dynamic System Involving the -Laplacian on Time Scales

We establish several new Lyapunov-type inequalities for some quasilinear dynamic system involving the -Laplacian on an arbitrary time scale , which generalize and improve some related existing results including the continuous and discrete cases.

[1]  S. Hilger.  Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .

[2]  Allan Peterson,et al.  Discrete Hamiltonian Systems , 1996 .

[3]  B. G. Pachpatte,et al.  On Lyapunov-Type Inequalities for Certain Higher Order Differential Equations , 1995 .

[4]  Stefan Hilger,et al.  Differential and difference calculus — Unified! , 1997 .

[5]  Xiaofei He,et al.  A discrete analogue of Lyapunov-type inequalities for nonlinear difference systems , 2011, Comput. Math. Appl..

[6]  Devrim Çakmak,et al.  Lyapunov-type inequality for a class of Dirichlet quasilinear systems involving the (p1,p2,…,pn)-Laplacian , 2010 .

[7]  Juan Pablo Pinasco.  Lower bounds for eigenvalues of the one-dimensional $p$-Laplacian , 2004 .

[8]  Xiaofei He,et al.  Lower bounds for generalized eigenvalues of the quasilinear systems , 2012 .

[9]  Zhimin He,et al.  Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales , 2004 .

[10]  Zhan Zhou,et al.  Lyapunov inequality for linear Hamiltonian systems on time scales , 2005 .

[11]  Samir H. Saker,et al.  Oscillation of nonlinear dynamic equations on time scales , 2004, Appl. Math. Comput..

[12]  Stanley B. Eliason,et al.  A Lyapunov Inequality for a Certain Second Order Non‐Linear Differential Equation , 1970 .

[13]  Aydin Tiryaki,et al.  On Lyapunov-type inequality for quasilinear systems , 2010, Appl. Math. Comput..

[14]  Martin Bohner,et al.  Lyapunov inequalities for time scales , 2002 .

[15]  M. Ünal,et al.  Lyapunov-type Inequalities for Certain Nonlinear Systems on Time Scales , 2008 .

[16]  Ravi P. Agarwal,et al.  Lyapunov and Wirtinger inequalities , 2004, Appl. Math. Lett..

[17]  Xiaofei He,et al.  On inequalities of Lyapunov for linear Hamiltonian systems on time scales , 2011 .

[18]  Jean-Luc Akian.  A SIMPLE PROOF OF THE ELLIPTICITY OF KOITER'S MODEL , 2003 .

[19]  Xiaojing Yang,et al.  Lyapunov-type inequality for a class of even-order differential equations , 2010, Appl. Math. Comput..

[20]  C. Ahlbrandt,et al.  Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations , 1996 .

[21]  A. M. Li︠a︡punov.  Problème général de la stabilité du mouvement , 1949 .

[22]  Stanley B. Eliason,et al.  Lyapunov Type Inequalities for Certain Second Order Functional Differential Equations , 1974 .

[23]  Xiaojing Yang,et al.  On inequalities of Lyapunov type , 2003, Appl. Math. Comput..

[24]  Lucas Jódar,et al.  A Lyapunov inequality for a second order nonlinear differential equation , 2011, Appl. Math. Lett..

[25]  Ravi P. Agarwal,et al.  Half-linear dynamic equations , 2003 .

[26]  Qi-Ming Zhang,et al.  Lyapunov inequalities and stability for discrete linear Hamiltonian systems , 2011, Appl. Math. Comput..

[27]  Xiaojing Yang,et al.  On Liapunov-type inequality for certain higher-order differential equations , 2003, Appl. Math. Comput..

[28]  A. Liapounoff,et al.  Problème général de la stabilité du mouvement , 1907 .