Eigenvalue Comparisons for Second-Order Linear Equations with Boundary Value Conditions on Time Scales

This paper studies the eigenvalue comparisons for second-order linear equations with boundary conditions on time scales. Using results from matrix algebras, the existence and comparison results concerning eigenvalues are obtained

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our result

Uniqueness of Periodic Solution for a Class of Liénard p-Laplacian Equations

By topological degree theory and some analysis skills, we consider a class of generalized Liénard type p-Laplacian equations. Upon some suitable assumptions, the existence and uniqueness of periodic solutions for the generalized Liénard type p-Laplacian differential equations are obtained. It is significant that the nonlinear term contains two variables