On Lyapunov inequality in stability theory for Hill's equation on time scales
نویسندگان
چکیده
منابع مشابه
Lyapunov-type inequality for a higher order dynamic equation on time scales
The purpose of this work is to establish a Lyapunov-type inequality for the following dynamic equation [Formula: see text]on some time scale T under the anti-periodic boundary conditions [Formula: see text], where [Formula: see text] for [Formula: see text] and [Formula: see text], [Formula: see text] with [Formula: see text] and [Formula: see text], p is the quotient of two odd positive intege...
متن کاملLyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales
with A. being a given m × m-matrix function, has been an intensively discussed field in both theory and practice. This problem can be seen in many real problems, such as in electric circuits, chemical reactions, and vehicle systems. März in 1 has dealt with the question whether the zero-solution of 1.1 is asymptotically stable in the Lyapunov sense with f t, x′ t , x t Bx t g t, x′ t , x t , wi...
متن کاملAnderson's inequality on time scales
We establish Anderson’s inequality on time scales as follows: ∫ 1 0 ( n ∏ i=1 f σ i (t) ) t ≥ (∫ 1 0 (t + σ(t))n t )( n ∏ i=1 ∫ 1 0 fi (t) t ) ≥ ( 2n ∫ 1 0 tn t )( n ∏ i=1 ∫ 1 0 fi (t) t ) if fi (i = 1, . . . , n) satisfy some suitable conditions. c © 2005 Elsevier Ltd. All rights reserved.
متن کاملTheory of hybrid differential equations on time scales
In this paper, we develop the theory of hybrid differential equations on time scales. An existence theorem for hybrid differential equations on time scales is given under Lipschitz conditions. Some fundamental fractional differential inequalities are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the compa...
متن کاملHermite-Hadamard Inequality on Time Scales
Recently, new developments of the theory and applications of dynamic derivatives on time scales were made. The study provides an unification and an extension of traditional differential and difference equations and, in the same time, it is a unification of the discrete theory with the continuous theory, from the scientific point of view. Moreover, it is a crucial tool in many computational and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2000
ISSN: 1029-242X
DOI: 10.1155/s1025583400000333