A Lyapunov-type stability criterion using ^{} norms

By Meirong Zhang, Weigu Li. 2002

81 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/63a91b73de4697f3cf5309874e3a33e95012b43c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Haiyan Wang
2. Meirong Zhang
3. Pedro J. Torres
4. X. Tang
5. Gang Meng
6. Qiaoling Wei
7. Jifeng Chu
8. N. Fan

In Control and Systems Engineering

1. Haiyan Wang
2. Pedro J. Torres
3. X. Tang
4. Gang Meng
5. Meirong Zhang
6. Jifeng Chu
7. Daniel Franco

In Mathematical Physics

1. Gang Meng
2. Meirong Zhang
3. X. Tang
4. Qiaoling Wei
5. Pedro J. Torres
6. Haiyan Wang
7. Xianhua Tang
8. Nikolaos S. Papageorgiou

Citations in the corpus

• Twist periodic solutions of repulsive singular equations (2004, background): “In this case, the linearized equation y′′+gx(t; x(t))y=0 is stable as a consequence of the main result of [22].”
• Extremal values of smallest eigenvalues of Hill's operators with potentials in L 1 balls ✩ (2009, unknown): “Some nice works on estimates of eigenvalues are [1,6–8,12,14,26,28].”
• Extremal values of eigenvalues of Sturm-Liouville operators with potentials in L 1 balls (2009, background): “See also [23] for their role in the stability of Hill’s equations.”
• Lyapunov inequalities and stability for linear Hamiltonian systems (2012, methodology): “See [36].”
• Positive periodic solutions of singular systems with a parameter (2010, background): “(0) ≤ G(t,s) ≤ Gˆ( T 2 ) = sin kT 2 k(1− coskT) = 1 2ksin kT 2 for s,t ∈ [0,T]. The same estimates can also be found in [11,19,25]. For a nonconstant function ai(t), there is a criterion discussed in [25,31] to guarantee the positiveness of the Green’s functions. Therefore, we always assume the foll”
• Certain classes of potentials for p ‐Laplacian to be non‐degenerate (2005, methodology): “Very recently, this has been generalized to the L, 1 ≤ α ≤ ∞, cases by Zhang and Li [18].”
• A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle (2003, unknown): “The second author is supported by the NNSF, the National 973 Project and the Excellent Personnel Supporting Plan of the Ministry of Education, China.”